In the literature, interoperability is often informally defined in terms of the achievement of coordination among diferent parties in the accomplishment of some goals, ranging from the efective transmission of knowledge, usually about the world, to the execution of practical tasks. However, it is not clear whether adopting a shared ontology, or, in general, reaching an agreement on semantics, is either a necessary, or suficient, condition to that end. In this paper, we set out to explore this topic by outlining an approach resting on minimal epistemological assumptions, questioning to which degree coordination capabilities usually associated with high-level cognitive functions (e.g., language) can be recovered in the proposed setting. It is suggested that our approach might also provide fruitful grounds for machine-learning-enhanced methodologies.
Semantic technologies are widely recognized as foundational to interoperability, as they provide standardized, machine-readable representations of data and knowledge, facilitating shared understanding, integration, and reuse. However, the notions of interoperability and semantics are employed and understood in markedly diferent ways in the literature. As such, despite the assumed centrality of their connection in knowledge representation and applied ontology, the relationship between the two remains opaque at best. This conceptual variability motivates a critical examination of the presumed connection, both to clarify the foundations of orthodox approaches and to explore the viability of alternatives.
In this paper, we undertake this endeavor by raising the question of whether agreement on a
theory’s semantics, or the endorsement of a shared worldview, is suficient, and/or necessary, to achieve
coordination among a plurality of agents. Following a brief survey of how the core notions are employed
in the literature and an outline of key concerns regarding their presumed interrelation (Sect. 2), we
address these questions by outlining an alternative approach grounded in minimal epistemological
assumptions, looking back to philosophical tenets at the heart of the so-called “upward path to structural
realism” [
The underlying theoretical foundations and the formalization of the framework are presented in Sect. 3 and Sect. 3.1, respectively. Sect. 4 focuses on illustrative examples, which are followed by an exploratory discussion (Sect. 4.1). Here, we touch on broad epistemological issues related to the capability of situated epistemic agents to navigate and make sense of the world. While considerations pertaining to cognition and communication are certainly relevant, our main focus lies in the acquisition, transmission, and aggregation of data for the purposes of coordination, prediction, and intervention. We suggest that data acquired adhering to the epistemological stance at the core of our approach may ofer a fruitful basis for machine learning. Conversely, the integration of machine-learning-enhanced methodologies within this framework represents a promising avenue for future research.
In the literature, interoperability is frequently understood, implicitly, if not explicitly, in terms of the
ability to enable information or meaning exchange and to support coordination among systems, that is,
the achievement of shared goals or the cooperative execution of tasks [
The gap between these two notions becomes evident when one adopts a theory of meaning according to which real-world semantics cannot be fully captured intra-linguistically. From a referentialist perspective, scholars who agree on the truth values of sentences (of a logical language), may associate these sentences with radically diferent states of afairs in the world, possibly adopting diferent domains of interpretation. Logical semantics constrains the interpretation of theories, but it always leaves room for diferent real-world interpretations. Therefore, outside of a strict, intra-linguistic theory of meaning (such as inferentialism), sharing a theory—e.g., a computational ontology including its factual and terminological axioms—does not guarantee semiotic interoperability and may lead to coordination failures. The situation worsens when the interpreters are not granted direct access to the structure of the world or to the very same conceptualization of it. This is not to say that ontologies do not facilitate semiotic interoperability. Rather, it is a way to emphasize the importance of tacit agreements and alignments among users. Meaning negotiation and calibration are just as important in semantic technologies as they are in ordinary communication. Presupposing alignment due to the sharing of ontologies might lead to costly (and hard to detect) mistakes.
Indeed, coordinating or exchanging information among agents does not seem to require the sharing of worldviews. Consider, for instance, two people, and , who speak entirely diferent languages and have radically divergent worldviews: believes in Greek gods, while considers themselves to be in a skeptical scenario and posits nothing but a series of states of a matrix. Now suppose systematically utters the sentence “Zeus is in bad mood” before it starts raining. In time, might learn to associate ’s utterance with the onset of rain—which understands as a transformation in the matrix’s state—despite the fact that does not share ’s worldview and would not accept the posited entities and states of afairs. In fact, it is irrelevant to whether is a human being uttering sentences according to a complex theory of the world or a barometer: insofar as reliably tracks states of the world, and is able to form a consistent association between certain perceived outputs of and the latter, information about the world is efectively transmitted, and made available for planning and intervention.
The extent to which coordination and communication can be achieved without a shared language, semantics, or ontology remains an open question. In what follows, we introduce a formal framework to study this question without presupposing any kind of semantic sharedness.
At the dawn of the 20ℎ Century, several prominent philosophers sought a way to provide a foundation
for both scientific inquiry and metaphysical investigation within a realist (as opposed to idealist, then
prevalent) framework: a foothold in the external world withstanding Kant’s challenge. In this context,
Poincaré [13] and Russell [14]—the latter drawing on the work of Meinong [15, 16]—courted the idea
of there being a structural similarity between the noumenal, how things are in themselves, and the
phenomenical, postulated to explain the pragmatic efectiveness of our commonsensical worldview and
our scientific theories. 1 If granted, this structural similarity provides us with an access to the world in
itself, albeit in a limited and indirect fashion: relations holding among the objects in one’s experience
are the mirror of relations among external world entities—which ground, and constrain, all the possible
representations having them as focus. Diferences among entities are thus not created via comparison,
but are merely apprehended by means of it. This guiding intuition lies at the heart of the so-called
Helmholtz-Weyl Principle (hereafter HWP ), which Psillos and Votsis regard as a cornerstone in the
“upward path” to epistemic structural realism [
Much ink has been spilled on Russell’s understanding of the HWP . For our purposes, we will assume that (1) from an ontological point of view, the principle comes down to an injective mapping : p qztHu between the set of perceptions and sets of possible states of the world ( is the set of all the possible states), such that the sets in the co-domain are disjoint, i.e., states of the world univocally determine perceptions.2 (2) From an epistemological point of view, a situated epistemological agent is warranted to infer, from the fact that they had a certain perception, rather than others, that that which is perceived (the world) is in a certain set of states, rather than others. It should be stressed that, in this case, the agent can only discriminate contrastively between said sets, being completely blind to the states of the world themselves, as well as to which states fall within which set. Perceptions can be thus seen as partitioning the logical space in a way reminiscent of Rayo’s characterization of propositions [18].
So understood, the principle arguably has considerable intuitive plausibility. Consider a simple case involving a human being having a perception of redness: for such a perception to occur, the world has to be in a state that falls within a certain range; conversely, for the subject to perceive a diferent color, the world would have to be in a diferent range of states, one that does not include the actual state. Intuitively, perceptions allow us to navigate the world by tracking diferences which are relevant to us; if something like the HWP did not hold, our capability of doing so, as well as the diferences among perceptions, would be in need of alternative explanations. It should be noticed that in this framework a perception is naturally compatible with the world being in states difering from the actual one, insofar as the perceiver is not capable of discriminating between them:3 this can be either due to a standard lack of sensibility/precision (e.g., the human’s perceptual apparatus reacting in the same way to slight diferences in electromagnetic spectrum), or because the diferences are not “relevant” (e.g., causally disconnected worldly diferences), yet skeptical scenarios are also relevant (e.g., brain-in-a-vat scenarios in which the human being is stimulated so that they perceive redness). Indeed, these distinctions make sense only within a certain theoretical framework or within a certain worldview positing things which go way beyond what is warranted by the HWP , as interpreted by us.
It is no coincidence that the HWP emerged during a period strongly influenced by Mach/Duhemstyle instrumentalism, holding scientific theories as symbolic tools for eficiently organizing sensory experience—instruments for making predictions and guiding action rather than attempts to uncover the supposed metaphysical structure underlying phenomena or to attain truth in that sense. In fact, the HWP , taken at face value, hints at an even more radical epistemological approach: one that does not commit to any particular theory of the world (not even as a way to “keep the score”) and resting on minimal, revisable assumptions concerning how perceptions are connected—operating entirely at that level. This marks a departure from the traditional Galilean method, hinged on idealization and 1It is worth noting that, in his time, Kant faced criticism for positing a dependence of the phenomenal on how things are in themselves: critics argued that this move involved a misapplication of the category of causation beyond its legitimate domain, namely, the realm of possible experience. Arguably, this “unwarranted assumption” is key in the cited authors’ proposals. 2Focusing on world states allows to sidestep issues concerning the identification of entities, and structure in general, in the world, among other things. 3Only given a perceiver capable of discriminating between each and every diferent state of the world there can thus be an isomorphism between phenomena and noumena (and, thus, representations carrying maximal information—i.e., singling out a single possible state of the world in contrast with all others). That said, the converse of the HWP gets problematically close to idealism, positing a systematic dependence of the world on perceptions. controlled observation, insofar as matters of saliency (i.e., which entities/characteristics of a system are counter-factually relevant to answer a certain experimental question) and granularity in description presuppose a (somewhat) rigid theoretical framework. The upside of accepting these challenging restrictions is a solid metaphysical foothold hinged on a minimal principle playing an explanatory role: information about the world (being in a certain range of ways rather than others), contra certain strongly anti-realist versions of instrumentalism. Operating at such a level putatively sidesteps issues concerning the underdetermination of theories, and the need to establish connections across representational frameworks—this being extremely relevant for knowledge representation and interoperability.
While another movement inspired by instrumentalism, Logical Positivism, failed as a descriptive project targeting natural languages and scientific theories, one can envision a system taking some of its core principles as prescriptive guidelines in order to improve the transmission of information about the world across a network. The reasoning underlying the proposal is simple. Going back to points discussed in the previous sections: (1) if, necessarily, symbolic systems leave room for diferent interpretations, it might be worth shifting the focus towards mechanisms which connect pairs of perceptions in a way which robustly allows the second perceiver to produce actions whose success relies on the world being in a certain range of ways rather than others, as tracked by the first perception; (2) if our epistemological position prevents us from adjudicating between competing theories—assuming that one (or more) is correct—yet the theoretical assumptions in question are not critical (and sometimes an obstacle, due to unwarranted assumptions of standardization and rigidness in adjustments) for interoperability, then we should operate at a level of abstraction where data is as theory-neutral as possible.
The idea can be made more precise by comparison with instrumentalism. Point (1) invites us to assume a physicalist standpoint, shifting the focus from perceptions to the state of a generic portion of the world functioning as an observational apparatus and capable of being influenced, and influencing, states of the world. This also allows us to sidestep issues related to perception which clearly go beyond the scope of this brief paper. Indeed, assuming a physicalist standpoint, HWP should be even less contentious, as it can be read as simply stating that one is warranted to posit a correlation between two states of the world when one causes the other, with cascading consequences concerning the state of portions of the world—which can be taken to be “observational apparatuses”, since they are influenced by the world, and “agents”, since they influence it. It is now worth pointing out that, in order for the connections to be “informative”, the state of the observational apparatus has to be non-trivially determined by factors which do not include the observational apparatus’ state itself. This is implicit in the causal formulation of the HWP , given the assumption of a temporal asymmetry of causes and efects. However, to avoid the metaphysical commitments and conceptual baggage associated with causality, the principle can be more neutrally reformulated in terms of dependence. For our purposes—and endorsing the simplification with respect to time for the sake of simplicity—the core intuitions underlying the HWP are thus better expressed as follows:
P2 Let time 1 precede time 2. The state of the world at 2 depends on, and is determined by, its state at 1, i.e., diferent states of the world at 2 imply diferent states of the world at 1. (Revised Helmholtz-Weyl Principle)
According to (P2), the state of an observational apparatus is correlated with a range of possible states of the world, which determine it (if they hold). Diferent states of stand for, and “reveal”, disjoint ranges.
In focusing on mechanisms which might, or might not, involve humans, and denying them a special place in the system, our proposal radicalizes tendencies for externalization which are shared by approaches focusing on sensors (for data acquisition) and machine learning (for data aggregation), which are usually characterized by the attempt to fit in with human conceptualization. In general, the externalization and standardization of data acquisition is a defining feature of the scientific enterprise and arguably one of the key reasons for its pragmatic and predictive success. As widely acknowledged in the literature, new theories and new instruments often co-evolve, and the mediation of instruments is not only essential for detecting world-states beyond the reach of human senses, but also to decide between diferent competing theories [19, 20].
Another comparison, this time with the operationalist derivations of instrumentalism, can shed light on (2). To improve information transmission and data quality, operationalist approaches ground meaning on procedures of data acquisition. Since no two measurements are alike, one might ideally want to include as much contextual information as possible to define these procedures precisely. However, including all the contextual information is not feasible and doing so would also prevent generalization. Notably, similar tendencies are echoed in the increasing focus on context regarding data (metadata and provenance in primis). Unlike these approaches, our framework does not distinguish between the target and the context when determining the state of an observational apparatus; both contribute. Thus, the issue shifts to “transmitting” and “aggregating” the states of the individuals in the world in a way that allows for efective predictions. Accordingly, our focus turns pq to observational apparatuses that discriminate between diferent (sets of) states of the world by entering distinct internal states in response to them (possibly keeping track of past observations); and pq to mechanisms that reliably correlate the internal states of diferent observational apparatuses producing interventions in the world that yield expected (observable) results. Notice that our approach, which we will now illustrate with concrete examples, has precedents in this regard and shares similarities with the proposal advanced by Berto, Rossi & Tagliabue [21], as well as with previous work in cybernetics and robotics.
To concretize the ideas outlined in the previous section, we introduce a framework that lays the foundation for an exploratory discussion on the potential developments of this approach. For our purposes, we start by outlining a framework that generalizes basic cellular automata (CA) [21], and subsequently examine simple toy models constructed within this generalized setting. Compared to CA, our framework aims to provide a more detailed and dynamic model of a world whose inhabitants (CAs’ cells) are not necessarily eternal, can change their configuration through time, and can be governed by specific laws. The following defines our general framework: • We adopt a discrete set of times and a set of (internal) states that describe the states of a set (called the domain) of individuals. To simplify the notation, we assume that is a subset of the set of integers, writing 1 for the successor of and 1 for its predecessor. • The (total) function : p q identifies the temporal extension of an individual, i.e., the set of times at which an individual exists. We assume that for all P , pq H , i.e., all individuals exist at least at one time. • The (partial) function : identifies the state of an individual at a time at which it exists. This function enables tracking of entities’ internal state through time.4 We assume that for all P , then P pq if and only if there exists P such that p, q . • The (total) function : pq identifies the base of an individual at a time at which it exists, i.e., the set of individuals (called bases) on which depends at . This function establishes (directed) connections between individuals, i.e., it determines the “shape” of the world. Since individuals can change their inputs over time, the shape of the world is not necessarily static. • The world is regulated by discrete dynamics: the state and the bases of an individual at time are fully determined by pq the states of the bases of at time 1 and pq the deterministic updating rules that regulate the world. These updating rules can impact both the states and the bases. This means that the base of represent the part of the domain that influences ’s state. The manner in which this influence is implemented depends on the specific rules considered. The framework allows for independent individuals who do not have bases and whose behavior is regulated by internal rules that do not depend on other individuals.
Notably, our framework also allows for scenarios in which individuals have “private” states—i.e., if , then for all P pq and 1 P pq , we have that p, q p, 1q—and are regulated by “private” updating rules, i.e., each individual has its own specific way of functioning. It is thus possible to tune the framework to accommodate both “reductionist” assumptions implicit in classic CA, where individuals 4The function can be made total by introducing a state that characterizes all the individuals that do not exist at a given time. resemble Aristotelian matter and laws are universal, as well as scenarios populated by haecceities, with no room for ontologically grounded abstractions. Intermediate configurations are also possible: for instance, the domain could be partitioned into subdomains (types of individuals) 1, . . . , , with updating rules parameterized relative to these types. This flexibility is significant not only because inhomogeneous worlds cannot be dismissed a priori, but also to investigate the conditions under which a situated individual can efectively navigate and acquire knowledge about the world it belongs to. Showing that, under certain (epistemological) assumptions, an individual’s capacity to navigate its environment depends on some form of Millian “uniformity in nature” would arguably be a noteworthy result in itself. Naturally, the framework can be adjusted further by introducing additional constraints. For example, one could stipulate that all individuals are interconnected or have nonempty bases.
In order to better describe the examples, we distinguish the following types of individuals, each represented with a distinct graphical notation as detailed below.
• Memory (diamond nodes ). Individual is a memory of individual at time if the state of at time depends only on the states of and of at 1 (p, 1q t, u ) and the state of at 1 depends on the states of at ( P p, q ). The state of a memory depends on its previous state, creating a cycle (see in Fig. 1). • Agent (circle nodes ). Individual is an agent at time if and only if is not the memory of any individual at and there is a single that is a memory for at . We assume that memories cannot be shared by several agents. The memory of agent aggregates the current states of and , providing the result of the aggregation as input for the agent at the next time step. This captures the “introspective” nature of agents: their state depends not only on the states of “external” individuals, but also on their own previous internal state. In our models, memories act as externalizations of agents’ internal states and dynamics. This design enables the modeling of more complex processes with varied temporal extensions. • Sensor (rectangle nodes ). Individual is a sensor of agent at time if and only if pq is in the base of at ( P p, q ); pq does not have a memory at ; pq is not the memory of any agent at . Sensors do not have memory, so their state depends only on the states of “external” individuals (directly or indirectly) connected to them. However, note that the agents do not have direct access to the states of the sensors (they are only influenced by them), nor do they know which portions of the world the sensors are afected by, or how reliably they track certain (sets of) world configurations. The whole battery of sensors of an agent is its console. Agents can share sensors, or have sensors that are connected to the sensors of other agents.
In general, insofar as all individuals receive inputs and produce outputs, they can all be considered as “reasoners” or “performers of computations”, given a broader understanding of these notions.5 Without aiming to fully capture the notion of agentivity, the previous “structural” characterizations of agents, memories, and sensors are suficient for our illustrative purposes and they avoid committing to complex cognitive architectures or specific ontological analyses.
Let’s now consider some simple examples. For simplicity, we will assume that all the individuals exist and have the same bases at all times (for all P , pq and : pq).
Example 1 (redness sensation of human ). To familiarize with the framework, we consider the simple graph in Fig. 1 where the nodes stands for individuals, i.e., t 1, 2, 1, 2, , u, and the arrows indicate the bases of individuals, i.e., p 1q H , p 2q H , p 1q t 1u, p 2q t 2u, pq t 1, 2, u, pq t, u . According to the above definitions of types of individuals, at all times, except the first and last ones, is an agent; is a memory of ; 1 and 2 are sensors of . For simplicity, we consider only 5 times: t0, 1, 2, 3, 4u and we mainly focus on times 1, 2, 3, where the previous definitions are efective. We introduce states in as needed. Fig. 1 shows the subset of relevant for the following discussion. In this figure, node is labeled : when p, q .
We informally describe the example as: the human has memory , visual apparatus 1 which is afected only by 1, a part of the world not further specified, and auditive apparatus 2 which is afected by 2, a part of the world diferent from 1. State assures is in visual rest while state assures 5This option is for instance favored by [21].
1 |10:: 12 2 |10:: 34 1 |21:: 65 2 |21:: 87 |32:: |21:: 910 has a redness sensation. The interpretation of states 1- 10 is left unspecified. With the intuitive interpretation in mind, let us follow the evolution of the system in our example. The stimulation of the visual apparatus is modeled via the transition of 1 from 5 (at 1) to 6 (at 2). Since only the part of the world 1 is in the base of 1, the transition of 1 is fully determined by the transition of 1 from 1 (at 0) to 2 (at 1). Similarly for the stimulation of the auditive apparatus 2. The state of the human being is afected by the states of their perceptive apparatuses 1 and 2 as well as memory (pq t 1, 2, u). The contemporaneous transitions of 1 from state 5 (at 1) to state 6 (at 2), of 2 from 7 to 8, and of 1 from 9 to 10 determine the transition of from visual rest (at 2) to redness sensation (at 3). l
Ex. 1 allows us to make some general considerations about our framework. First note that our framework is compatible with two perspectives: pq a descriptive one, in which one describes the state and the shape of the world (i.e., the states and bases of all individuals) at all the times, but the updating rules remain implicit (we adopted this perspective in Ex. 1); and pq a constructive or simulative one, in which the updating rules are explicit, and the state and shape of the world is generated step by step via such rules, starting from an initial configuration. Perspective pq is clearly weaker than perspective pq. Epistemological approaches typically exclude exact knowledge of the rules that govern the world, which can only be inferred inductively a posteriori.
Second, both perspectives presuppose knowledge of the world’s structure, i.e., the dependencies between individuals. This knowledge enables the study of how states propagate within a given world. For instance, in Ex. 1, the state of the visual apparatus 1 is only afected by the state of 1. Hence, 1 tracks the state of 1 at a previous time without interference, i.e., the state of 1 can be systematically calculated from that of 1, preserving information about the range of configurations of the world to the degree that 1 can discriminate between diferent states of 1. For example, 1 could enter the same state despite 1 being in several diferent states. In this case, 1 clusters diferent states of the world, but it does that in a systematic way. The same applies to the agent when considering their visual apparatuses and memory. That is, given the resolution disposes of, systematically tracks the configurations of the states of 1, 2, and . Ideal channels (and fibers), as defined below, generalize the idea of reliable tracking by considering chains of tracking steps.
• Ideal channel and fiber. At time , x1, . . . , y with , tu , and ¥ 2, is a (transmission) ideal channel of length 1 ending in if and only if, for 0 ⁄ ⁄ 2 , pq 1 P p, q and pq for all P , p, q 1 or p, q X 1 H. A fiber is an ideal channel with the form xt 1u, . . . , tuy.
First of all, 1 contains all the direct “inputs” (the bases) of the ending individual at . Thus, ideal channels of length 1, which have the form xp, q, tuy , formally capture the examples discussed above: xt1u, t1uy (a fiber), xt2u, t2uy (a fiber), xt1, 2, u, tuy, and xt, u, tuy are the only ideal channels of length 1 (at all times except 0) in Ex. 1. Secondly, 2 collects some of the inputs of “mediated” by at least one of its bases, i.e., as stated in clause pq, 2 is a subset of the union of the bases (at 1 ) of the bases of (at ). Clause pq assures that when an input mediated by P p, q is included in 2 , all of ’s other bases (at 1 ) are also included in 2 , i.e., all bases are included in the channel as mediated inputs of . It is however possible to exclude all the bases of an P p, q from 2 . In this case, is considered a “starting point” of the channel. Similarly, when has no base. This procedure is iterated until 1 is reached, which allows the channel to collect inputs mediated by 2 layers of individuals. Formally, the set of the starting points of channel x1, . . . , y is 1 Y 1 t | P and pq X 1 Hu . Intuitively, the ending individual of an ideal channel tracks (with a given resolution) the states of the starting points of the channel.
In Ex. 1, both xt1, 2, , u, t1, 2, u, tuy and xt1u, t1, 2, u, tuy are ideals channels of length 2 ending in (at all times except 0). As we have seen, in general, the state of at 1 depends on the states of all its bases at (which are included in 1 ). Thus, ’s redness sensation is, in principle, afected also by the state of ’s auditory apparatus and by past sensations stored in memory—i.e., all the context is included. In our framework, memories can thus provide a way to model environmental adaptation, that is the production of varied outputs in response to otherwise identical external sensory inputs. This is a desirable feature when human and artificial agents, qua agents, are involved, as per our example. The framework is likewise capable of modeling robustness: measurement devices are typically designed to be more sensible to diferences in the state of certain (posited) bases and, conversely, to minimize the impact of others, usually including memories. Memories can thus be used to model the internal states of devices due to repeated excitations or permanent deformations (e.g., wear). A robust device either controls the states of interfering bases (the noise) or compensate for their impact on the states of its inputs. In the first case, the (update function of the) device may be insensitive to the states of interfering inputs within certain environmental conditions (in controlled environments, the device can control them, at least partially). In the second case, the (update function of the) device may take interferences into account, adjusting its output state based on this information.
The concepts of ideal channel and fiber can be exploited to model more complex correlations among the states of two individuals at diferent times, also taking into account the world’s initial/possible states and the rules of update. These correlations are especially interesting when shifting from an external view of the system to a situated epistemological perspective, as they appear necessary to explain how an agent could perform efectively with limited access to the external world and restrictive epistemological constraints. As mentioned in the previous sections, adhering strictly to HWP means that when, in Ex. 1, has a sensation of redness at , they do not immediately gain information about the actual state of their sensors (and memories) or of the individual(s) that afected them. They also do not gain information about the number of the individuals in their base and in the world overall. They can only “know” that the world is in a certain range of ways rather than others, insofar as they have access to their (previous) internal states (e.g., via the memory) and assume that they are robust with respect to a subclass of their direct sensors. A little help from the world thus appears prima facie necessary to increase the position’s plausibility. Again, one should be careful not to be misled by the model’s apparent simplicity on this point. The range of the possible states for an agent can be extremely wide, and the agent may aggregate a huge number of inputs to produce a relevant output. Similarly, memories might encode complex structures, becoming progressively more complex via feedback loops, further enriching the agent’s behavioral repertoire. Additionally, Berto, Rossi & Tagliabue make a case for positing strongly reversible “worldly rules of transition”. According to the trio, diferent inputs cannot result in the same output (when it comes to the rules actually governing the world, though this might not hold for observational apparatuses which are actually composite mechanisms) and, their Turing-Machine-like world is time-reversal invariant [21]. As such, the ideas underlying the framework remain a promising avenue for exploration. Moreover, contrary to assumptions commonly endorsed alongside HWP on the upward path to structural realism, it does not seem necessary to postulate that agents have magically access to their ontological internal state for their behavior to be understood as an expression of knowledge about the world: memories show that an agent’s behavior can be afected by their knowledge about the world, even if they don’t have direct access to it. Conversely, as long as there is a mechanism that produces variable outputs by aggregating external inputs (without considering the previous states of a given agent or their memory), all the relevant functions appear to be expressed through behavior alone. Although our first example involved a human being’s perception of redness, the framework can be used to describe a non-sentient individual responding to environmental stimuli, such as a thermometer. In this respect, the model treats brains and hard disks as functionally analogous. One could even extend the analogy to include anything that keeps track of an individual’s previous states (previous ranges of states of the world—the states of an individual being especially salient). 1 3 1 1
5 2 3 2 4 2 4 1 2
In this section, we present two further examples of increasing complexity. Ex. 2 explores interactions involving inter-agent connections where one agent updates its memory and/or takes action based on sensors directly accessible only to the other. Ex. 3 highlights the expressive power of our framework and the proposed approach by addressing a more nuanced coordination scenario that incorporates dynamic updates and goal-driven behavior. As for Ex. 1, the intuitive descriptions for Ex. 2 and Ex. 3 are provided to help readers follow the examples and situate them in a concrete scenario. However, it is always possible to take a neutral and formal reading that does not go beyond the labels of the individuals and the dependencies depicted in the figure.
Example 2 (interaction between weather responsive windows 1 and 2 via light 5). This example illustrates how mechanistic connections between sensors (of diferent agents) can model oneway tracking and capture basic, yet meaningful, forms of “communication”. The notion of robustness is also further refined in the process. We consider the overall system in Fig. 2 designed to maximize home safety against adverse weather conditions by having one window anticipate adverse weather conditions based on the behavior of the other window. Informally, individuals 1 and 2 are two weather-responsive windows. Through sensor 1 (4), window 1 (2) indirectly accesses the weather condition of the portion of the sky above it, 1 (2). The closure of window 1 (2) turns on switch 3 (4). The physical light 5, partially under 1 and partially under 2, is designed to be on when one of the switches 3 and 4 is on and the other is of but its intended functionality is afected by the weather conditions of the portions of the sky 1 and 2. Window 1 (2) indirectly accesses the state of light 5 through sensor 2 (3). Memories 1 and 2 regulate the behavior of windows 1 and 2, respectively, through a feedback loop that keeps track of previously detected weather conditions. Windows 1 and 2 are in open or closed states (noted O/C); 1 and 2, as well as 1 and 4, are in good or bad weather states (noted G/B), while 3, 4 and 5, as well as 2 and 3, are in on or of states (noted ‘/a). l
Table 1 reports the states of the individuals in the system from time 0 to time 10 disregarding the dependencies of 5 on 1 and 2. The data in the table satisfy the informal update rules described above. Furthermore, for the moment, we do not consider the memories 1 and 2. We can then “interpret” the data in Table 1 using the intuitive reading of Fig. 2.
First, the closure of 1 at 3 can be attributed to the bad weather conditions that arose at location 1 at time 1. This dependence is tracked through the ideal channel xt1u, t1, 2u, t1uy,6 given that the state of 2 did not change from 1 to 2. Second, the switch of 5 at 5 can be attributed to the closure of 1 at 3, as tracked by the ideal channel xt1u, t3, 4u, t5uy, given that the state of 4 did not change from 3 to 4. Third, the closure of 2 at 7 (to maximize safety) can be traced back to the state of 5 at 5 through the ideal channel xt5u, t3, 4u, t2uy where 4 reports good weather at 2 at both 5 and 6. The last two dependencies can be composed to say that window 2 closes at 7 in response to the closure of window 1 at 3, i.e., the two windows “communicated”, as tracked by the ideal channel 6Given that in the examples the structure of the world is static, it is not necessary to temporally qualify the ideal channels. xt1u, t3, 4u, t5u, t3, 4u, t2uy with starting points 1, 4, and 3, given that the state of 4 did not from 3 to 4 and the state of 4 did not change from 5 to 6.
Assume now that p 2, 11q O given the states of 4 and 3 at 10. Assuming the stability of 1 and 2 and the previously described rules, it is easy to see that the state of window 2 commutes every four time steps. Memories play a fundamental role in avoiding this commuting. Consider then 1 and 2 and assume that the state of memory stores the last three states of . For example, p , q CCO indicates that the previous three states of were C, C, and O, where the first state in the list is the oldest. Since p 4, 0q G , p 3, 0q a and p 2, 0q OOO , there is no reason to update the state of 2 to C. This holds for 2 until time 5. At time 2, sensor 1 reports bad weather above 1. This is suficient to close 1 in the next time step. Since 1 does not change anymore, independently of the state of the memory, 1 remains closed. At time 6 the sensor 3 reports “disagreement” between the states of the switches 3 and 4. Since p 2, 6q OOO , 2 closes in the next time step because, three states ago, it was open while 1 closed. The situation is similar at times 7, 8, and 9. At time 10, we have that p 2, 10q CCC , p 3, 10q a , and p 4, 10q G . In this case, 3 reports that 1 and 2 were in the same state three time steps ago and 2 reports that 2 was in the state C three time steps ago. Therefore, even though p 3, 10q a and p 4, 10q G , it makes sense not to open 2, i.e., p 2, 11q C . Commutation of 2 is then prevented, given that 2 remembers the state of 2 from three time steps ago and the states of 4 and 3 take three time steps to propagate to 2.
Since there are no dependencies between 1, 2 and 5, xt1, 2u, t3, 4u, t5u, t2uy is an ideal channel with a single aggregation step (from 3 and 4 to 5). Now, introduce the dependencies of 5 on both 1 and 2. One might suppose that extreme weather conditions, such as lightning, could alter the behavior of light 5. This could cause 5 to be in the state a even if the states of 3 and 4 difer. In this case, given the ideal channel xt1, 2, 3, 4u, t5u y, 5 is not robust with respect to t3, 4u and this could indirectly afect the behavior of 1 and 2.
This suggests refining the notion of robustness of with respect to a given ideal channel ending in by focusing on certain ranges of the states of the starting points. In the previous example, one could exclude extreme weather conditions, by stating that robustness with respect to t3, 4u is guaranteed only when 1 and 2 are not in extreme weather conditions (i.e., provided that 1 and 2 are not in certain states). Alternatively, one could assume that pq 3 and 4 have multiple possible states that correspond to diferent degrees of “intensity” of being on or of; and pq extreme weather conditions do not impact the aggregation step provided by 5 when the intensity of its inputs exceeds a given threshold.
Finally, it is worth pointing out that, while this case might appear to be one involving predetermined compatibility, i.e., privileged one-to-one connections dependent on inherent similarities that facilitate mutual understanding, or ad-hoc interfaces between specific system types, similar exchanges are always possible insofar as one agent produces an output which can be reliably tracked by the other. There are thus no requirements concerning the agents themselves, but only the channels connecting them. 3 1 1 1 1 2 2 3 2 4 2 4
Example 3 (goal-directed coordination between agents 1 and 2). This example involves goaldirected coordination. Due to the complexity of the scenario we only provide an abstract description of the underlying processes omitting the formal details. We consider all the individuals and dependencies in Fig. 3. Informally, individuals 1 and 2 are concrete blocks which are in physical contact with each other. Individuals 3 and 4 are coolers/heaters connected to 1 and 2, respectively. Sensors 1, 2, 3, and 4 are analog mercury column thermometers. Agents 1 and 2 control coolers/heaters 3 and 4, respectively. Depending on the states of memories 1 and 2 and of thermometers on their private consoles, they set the level of activation of coolers/heaters. l
We start by considering a scenario in which sensors 2 and 3 are absent. In this case, the agents only have access to the state of the block afected by the cooler/heater that they control. Suppose also that 1’s goal concerns only the state of 1, and 2’s goal concerns only the state of 2. In this scenario, “coordination” is achieved only when the world behaves in a way that allows both agents to achieve their goals. For example, a situation where both the agents intend to keep the block more directly under their control at a temperature of 30 is plausibly achievable. The coolers/heaters can be activated for just enough time to reach the desired temperature, which can then be maintained with successive intermittent activations. Insofar as the temperatures of blocks 1 and 2 are similar, there is minimal energy exchange between them, resulting in a relatively stable system. Even when agents intend to maintain diferent temperatures for each block, both goals seem potentially achievable. However, the system is unstable due to energy transfer from the hottest block to the colder one.
A second scenario includes sensors 2 and 3. Still agent 1 acts directly only on the temperature of block 1, and 2 acts directly only on the temperature of block 2 but now both agents can monitor the temperature of the two blocks. In this scenario, the two agents share the goal of achieving a specific temperature configuration for the blocks, i.e., entering in respective states corresponding to the world being in a specific range of states. Here, coordination is intended in a more explicit and stronger way, i.e., as the sharing of a goal (in the previous scenario, each agent had a private goal). Suppose that the agents have the shared goal of setting the temperature of 1 to 70 and the temperature of 2 to 10 . This situation is similar to the one discussed in the previous scenario, but now the agents “know” the temperature diference between the two blocks. This information could support input-output relations characterizing the agentive system which more eficiently lead to the desired goals. However, it is unclear whether this increase in eficiency is solely due to the additional information or if the agents’ diferent goals also play a role.
Taking stock of the three examples discussed, and returning to the questions that motivated this inquiry, it appears increasingly plausible that, under reasonable mechanistic presuppositions about how worldstates depend one another, coordination does not necessarily require shared language, semantics or the endorsement of a common ontology (at least given the specifications of the notions we considered), but can also emerge from agential mechanisms being influenced, and influencing, the world in accordance with the world’s laws. In itself, this suggests that alternative approaches for the achievement of coordination, or relatively to the acquisition, transmission and aggregation of information about the world—approaches less tightly coupled to human-centric models of communication and cognition, but rather reminiscent of programming—might be worth considering and exploring.
Of course, the modeling of the examples is extremely simplistic in relation to our goals, and the results rest on various assumptions, leaving open reasonable doubts about whether coordination could be achieved in more complex toy-models, or in relation to more complex tasks or goals. In general, it might be questioned whether high-level cognitive functions (such as language use, theory-building, or conceptual abstraction) are ultimately (directly, or indirectly—via systems’ design) indispensable for coordination in real-world settings. However, rather than undermining the proposed framework, these doubts highlight what we take to be a productive line of inquiry. For instance, it appears pertinent to ask whether linguistic and cognitive function can fit within a mechanistic setting of information exchange—also connecting to questions currently raised concerning large language models. In this context, even hard-limits could reveal insights into how semantic artifacts could be improved.
One could consider the possibility of building (or aligning) artifacts fully bottom up, exploiting worldly connections to ensure that they reliably track world states.7 In relation to this point, other questions worth asking are whether, under which conditions, and to what degree, situated agents could “reverse engineer” their world’s structure given the minimal epistemological assumptions endorsed in our exploratory investigation: our framework, once expanded and adjusted, might provide a basis for practical work in this direction, examining toy models given diferent sets of constraints. Particularly interesting seems the application of techniques resting on machine learning—and much work has already been done in this direction in other contexts, such as robotics and data-driven scientific inquiry. Conversely, the kind of “minimal information” about the world resting on the HWP appears to provide solid foundations on which to apply such techniques, being as “raw” and less “theory-laden” as one can imagine. Nevertheless, even if such a project were viable, a connection between the resulting representations and human-friendly conceptual schemas or ontologies would likely remain necessary, if explainablity is to be retained, as suggested by [12].
In this paper, we critically examined the widely presumed foundational link between semantic technologies and interoperability, emphasizing how this connection is contingent upon how the latter is understood. Our analysis revealed salient conceptual divergences in the literature, which not only obscure the discussion but may also lead to misguided expectations among stakeholders. We argued that, insofar as “interoperability” is understood in terms of (the achievement of) coordination among systems, the adoption of a common semantic artifact (and endorsement of the encoded semantics) is neither a necessary nor a suficient condition—provided that coordination can undoubtedly be facilitated, and in some cases actually achieved, in conjunction with tacit agreements and prior alignments among agents, thus underscoring the importance of factual sharedness. What was initially taken to be a foundational link at the heart of the discipline, seemingly implicitly assumed across research programs, thus emerges as a complex interplay calling for deeper philosophical and practical scrutiny, and leaving room for the exploration of alternative approaches.
To those ends, we proposed a framework inspired by reflections central to the upward path to structural realism, focusing specifically on the Helmholtz-Weyl Principle, adapted to present purposes. Through (relatively) simple illustrative examples, we explored the extent to which coordination capabilities, typically associated with high-level cognitive functions, can be recovered within a purely mechanistic and deterministic setting, while emphasizing pragmatic aspects related to data acquisition, transmission, and aggregation. On the one hand, our approach moves towards demonstrating that coordination among diverse (not inherently-compatible), possibly non-sentient agents can be 7It is worth reminding that, from the point of view of a situated agent with no direct access to the states of a certain system, and of the world in general, this reduces to connections among perceptions at diferent times. Nevertheless, one is naturally free to produce revisable hypotheses concerning the underlying mechanisms. achieved without reliance on shared semantics or a common worldview. On the other hand, we hinted at the fact that, “raw information about the world”—resting on the presupposed capability of situated agents to reliably and objectively discriminate among diferent ranges of states of the world—might provide grounds for the bottom-up development of knowledge systems and agentive ones, or to connect disparate worldviews, theories, and, for what concerns us specifically, ontologies. While ontologies remain pivotal for explainability, especially for epistemic agents with limited cognitive resources, both apparent and factual agreement or disagreement can emerge at the level of constructed posits.8 Likewise, program-like mechanistic input-output connections grounded in worldly dependencies might ensure the achievement of coordination without relying on sharedness, but instead progressively leading to it.
While the purported results of our examples may not come as a surprise to those familiar with the cybernetics tradition, and are by no means definitive given the high-level nature of our models, they may nonetheless ofer thought-provoking insights for researchers in knowledge representation and applied ontology. We hope this work contributes to ongoing discussions about the epistemological and practical foundations of coordination, and encourages further exploration of alternative and complementary approaches, while at the same time improving conceptual clarity around interoperability. Needless be said, much work remains to be done to even just fix, let alone concretize, the ideas outlined in this exploratory paper, yet some of the points touched in the examples’ discussion, in relation to machine learning and the bottom-up engineering of knowledge systems, seem to us promising lines of research.
We would also like to thank three anonymous reviewers for their helpful comments to previous versions of this manuscript.
During the preparation of this work, the authors used M365 CoPilot and DeepL in order to: grammar and spelling check, paraphrase and reword. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content. 8Compare with [22, 23], which also present an approach to describe the relevant phenomena ontologically.
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