For descriptions of cognitive processes, including process models for research data provenance and simulation workow metadata, a formal notation is developed on the basis of the foundational ontological paradigm of mereosemiotics, i.e., the combination of mereotopology with Peircean semiotics. To demonstrate the viability of the approach, this is applied to extend the pre-existing OWL ontology for a physicalistic interpretation of modelling and simulation - interoperability infrastructure (PIMS-II) by a modal rst-order logic axiomatization.
Understanding and characterizing research workows, i.e., cognitive processes that yield a
research outcome, is essential to reproducibility [
The elementary multiperspective material ontology (EMMO), which is work in progress and
available as a beta version,1 is used as a foundational ontology [
The semantic artefacts mentioned above jointly rely on combining mereotopology with
Peircean semiotics, i.e., on the foundational ontological paradigm of mereosemiotics [
The following remarks are formally not part of the present axiomatization of mereosemiotics,
which is given in Sections 2.2 to 4.3. However, they may help to motivate the axioms and
provide a suggested interpretation for its concepts and relations on the basis of necessitism,
cf. the detailed discussion by Williamson [
It is proposed to construct the domain for the ontology as follows:2
1The name of that foundational ontology has recently changed, retaining the acronym “EMMO,” which had originally been introduced to abbreviate European materials and modelling ontology.
2Alternatively, where it is benecial to rely on a model that is enumerable, the domain can also be constructed 1. R4 is given an interpretation as dimensionless spacetime, with the rst three coordinates 1, 2, 3 of some four-dimensional point q = (1, 2, 3, 4) ∈ R4 being understood as spatial and the fourth coordinate 4 being understood as temporal. 2. ⊆ R4 is 4D-complete if and only if for each q ∈ there are linearly independent r1, r2, r3, r4 ∈ R4 such that q′ ∈ for all q′ − q = ∑︀1≤ ≤ 4 r where 0 < ≤ 1. 3. ⊆ R4 is simple if and only if it consists of nitely many connected components. 4. ⊂ R4 is 4D-delimited if and only if a) is a closed set and b) for some ∈ R, (q′ − q)2 ≤ 2 for all q, q′ ∈ and c) and R4∖ are 4D-complete and simple. 5. ⊂ R4 is temporally closed if and only if {4 | q ∈ } is a closed subset of R. 6. By some relation between physical and dimensionless spacetime, the physical universe is mapped to the connected 4D-delimited set ⊂ R4, the actual and necessary (dimensionless) universe; the employed relation should be such that its inverse, from to physical spacetime, is surjective and preserves continuity if physical spacetime is continuous, or adjacency if physical spacetime is discrete. It does not matter how exactly this is done as long as is 4D-delimited and consists of a single connected component, and as long as is the dimensionless universe necessarily; accordingly, by the present construction, is a continuum even if the physical universe is regarded as consisting of discrete elements.
As a closed set, includes its boundary, the three-dimensional hypersurface ⊂ . 7. The domain of the ontology is = { ⊂ ∖ | is 4D-delimited and temporally closed}. The elements of are that which exists; they are referred to as objects.3 8. An object ∈ is an item if it is a single connected component and a mereotopological collective if it consists of multiple connected components; in the latter case, the (maximal) connected components of are its mereotopological members.
9. For any two objects , ∈ , the criterion for proper parthood is P˙ ⇔ ⊂ , 10. the criterion for temporal precedence is given by ˓→t ⇔ ∀q ∈ ∀q′ ∈ : 4 ≤ 4′, 11. two objects temporally coextend, ≡ t, if and only if {4 | q ∈ } = {4′ | q′ ∈ }, 12. and the criterion for spatiotemporal connectedness is C ⇔ ( ∩ ) ̸= ∅. Accordingly, for any , ∈ , their spatiotemporal fusion is an object, ∪ ∈ . However, the universe does not exist ( ̸∈ ), an empty object does not exist (∅ ̸∈ ), and the complements of objects are not objects ( ∈ ⇒ ∖ ̸∈ ).
Ontological commitment, following Quine [33, paragraph 49], here extends exclusively to
individuals, namely, to objects as introduced above. That which exists is that which is accessible
to quantication in rst-order logic; this quantication is always over which will be omitted
for brevity. The inverse relation of Q will be denoted by Q− , and the product notation QQ′
will be employed for chain relations such that QQ′ ⇔ ∃ (Q ∧ Q′). Implementing
nominalism, existence is not attributed to concepts and relations, which are formalized here
as unary and binary predicates, not as individuals. However, textual labels corresponding
to concepts and relations, in particular, their internationalized resource identiers (IRIs), can
exist in the ontology; this construction is used in the OWL DL demonstrator implementation
PIMS-II [
3It is expected that research data infrastructures and digital platforms that employ the present ontology will
predominantly or exclusively deal with bona de objects as discussed by Vogt [
≡ ⊤
In the literature a great variety of potential axiomatizations of mereotopology have been explosed
in detail [
Q is the complete relation, and P˙ is idempotent, all of which simplies the system of mereosemiotic chain relations discussed in Section 4.1; necessitism and mereotopological essentialism support the discussion of modal relations, cf. Section 4.2.
Spatiotemporal connectedness C is reexive and symmetric [34] nothing is connected with everything, but all objects are connected indirectly ∀ C ∧ ∀(C → C);
∀∃ ¬C ∧ ∀ C2; C2 ≡ ⊤
Q is complete. C is constitutive of identity [34], proper parthood, and fusion [35] ∀ (∀(C ↔ C) → = ) , ∀ ︁(
(∀ (C → C) ∧ ̸= ) ↔ P˙ , ∀x (∀ ( x ↔ ∀(∨C ↔ C)) ∧ ∃ x) ; fusion here takes multiple arguments, x = 1 · · · being a sequence of ≥ Proper parthood P˙ is asymmetric and transitive, everything is a proper part of something, 1 variables. and P˙ P˙− ≡ ⊤
Q is complete (any two objects “underlap,” i.e., are joint proper parts of a greater object), all of which are deducible from Axioms (2), (4), and (5). As an expression of continuity of spacetime5 and the strong supplementation principle [36], ∀ ︁(
︁) ∀( P˙− P˙ → P˙− P˙) → P˙2 .
︁) ︁) (1) (2) (3) (4) (5) (6) (7) (8) The maximal items that are proper parts of a mereotopological collective are its members ∀ ︁(
Item: ∧ P˙ ∧ ¬∃′(Item:′ ∧ P˙′ ∧ P˙′) ↔ ≤ ˙ , ︁) and an object is an item6 if and only if it cannot be split into disconnected parts ∀ (∀(
→ C) ↔ Item:) . 4See the Appendix for a list of relations relevant to this work. 5By the construction from Section 2.1, this does not require actual physical spacetime to be continuous. 6See the Appendix for a list of concepts relevant to this work.
Temporal precedence ˓→t is asymmetric and transitive
¬∃(˓→t ∧ ˓→t) ∧ ∀ ((˓→t ∧ ˓→t) → ˓→t) , and it carries over from objects to their proper parts ∀ (︁ ˓→t → ︁( ∀′( P˙′ → ˓→t′) ∧ ∀′( P˙′ → ˓→t′)︁) ;
(9) (10) (11) (12) (13) (14) Axioms (9) and (10) entail that the relations P˙− P˙ and ˓→t are disjoint. Everything precedes something, everything is preceded by something, and by linearity of time, any two objects have proper parts that are in a temporal precedence relation with each other ∀∃ ˓→t ∧ ∀∃ ˓→t ∧ ∀∃′′ Temporal coextension ≡ t is dened by equivalent applicability of ˓→t to proper parts ∀ (︁ ∀′ ︁( ∃′( P˙′ ∧ ˓→t′ ∧ ˓→t′) ↔ ∃′( P˙′ ∧ ˓→t′ ∧ ˓→t′)︁) ↔ ≡ t ︁) , and ≡ t P˙− P˙ (equivalently, P˙− P˙≡ t) characterizes temporal overlap. so that it follows from Axioms (9) to (12) that ≡ t and ˓→t are disjoint. The chain ≡ t P˙ (equivalently, P˙≡ t) can be used to express that extends over a temporal subinterval compared to
The present approach to formalizing steps of a cognitive process as triads, inspired by Peirce [37,
38, 39, 40] and more recently Sowa [41, 42] and Goldbeck et al. [
↔ ∃123 3 123), ∀ 123 ︁( 3 123 ↔ (E˙1 ∧ ¨E2 ∧ E3 ) ,
︁) ... and E (isThirdElementIn) relate individual elements to the cognition. i.e., a cognitive step that has three elements, above, 1, 2, and 3, where 3 is a quaternary predicate..r.elating the three elements to the cognition; E˙ (isFirstElementIn), ¨E (isSecondElementIn),
It is not explicitly required here for any of these elements to be unique. On the one hand,
Peirce’s formulations would suggest this where he speaks of “the sign,” “the object,” and “the
interpretant” [38]. On the other hand, Peirce also develops the understanding that for every
semiosis, “there obviously are two objects, the object as it is in itself (the monadic object),
and the object as the sign represents it to be (the dyadic object)” and “also three interpretants;
7See also Francisco Morgado et al. [
Implementing semiotic monism [
∀(∃¨P ↔ Process:), and the part of the taxonomy that is relevant for the present purpose is given by9 ∀(Process: → Item:) ∧ ∀ (Cognition: → Process: ) ∧ ∀ (CognitiveStep: → Cognition: ) ∧ ∀ (TriadicCognition: → CognitiveStep: ) ∧ ∀ ((Perception: ∨ Interpretation: ∨ Metonymization: ) → TriadicCognition: ) . (17) The elements that act as a representamen (denoted R˙) in a cognitive step are engaged in representation (R, see above) with the elements that act as a referent (denoted O) in ∀ ︁( ( R˙ ∧ O ) → R .
︁) In a semiosis, these elements are the sign , the object , and the interpretant ′ [38] ∀ ′ ︁( (︀ 3 ′ ∧ (Perception: ∨ Interpretation: ))︀ → ( R˙ ∧ O ∧ R˙′ ) , (19) ︁) where and ′ act as representamina, and is their joint referent: The sign is the input of the cognitive step, the interpretant is its output, the object is what both are about.
A case distinction is needed for participation of triadic elements in triadic cognitions, by relation ¨P as introduced above, requiring physical presence and hence spatiotemporal overlap. Both perceptions and interpretations are semioses; what distinguishes them is whether or not 8In particular, if is included spatially in for some time, but not for all time, it means that and overlap. By virtue of spatiotemporal monism, there is no dualism of “continuants” (or “endurants”) and “occurrents” (or “perdurants”); in line with the EMMO, processes are not “perdurants,” and participants are not “endurants.” It is possible for the same object to be a process and to participate in a process.
9For denitions, cf. the Appendix and the ontology at http://www.molmod.info/semantics/pims-ii.ttl. (15) (16) (18) the object needs to be present. Representamina need to be present in general, whereas the referent only needs to participate in a perception ∀ ( R˙ → ¨P ) ∧ ∀ (︁ (O ∧ Perception: ) → ¨P .
︁) In a metonymization [45], a sign that represents is attributed to a new referent ′ ︁( ∀ ′ (3 ′ ∧ Metonymization: ) → (O ∧ R˙ ∧ O′ ) . ︁) Peirce requires a “real, physical connection of a sign with its object, either immediately or by its connection with another sign” [37]; a sign “must be aected in some way by the object which it signied or at least something about it must vary as a consequence of a real causation with some variation of its object” [39]. In particular, permitting the application of signs to contingent or hypothetical phenomena, Peirce states that a real causal connection is present if a “cause which precedes the event also precedes some cognition of the mind” [40, p. 142]; therein, the event (the occurrence of which may be contingent) is the referent, and the common cause is something that contributes causally to the occurrence of the event and to the cognition by which the representamen is generated. Accordingly, the “real causal connection” between the referent causal connection (hasCausalConnectionWith, denoted C˙⋆) with the new referent and the representamen needs to be preserved, i.e., it must be ensured that the old referent has a ︁( ︁) ∀ ′ (O ∧ O′ ∧ Metonymization: ) → C˙⋆′ .
The relation C˙⋆ is constructed as the reexive and transitive closure of the symmetric and antireexive relation hasDirectCausalConnectionWith (denoted C˙) ∀ (︁ C˙⋆ ↔ ︁(
︁) ∃( C˙⋆ ∧ C˙) ∨ C˙ ∨ = .
Constitutivity ¨C, cf. Axioms (41) and (42), participation ¨P, and direct grounding ˓→ (¨C ∨ ¨P ∨ ˓→ ∨ C˙) → C˙
∧ ¬∃ C˙, ︁) are sucient criteria for the presence of a direct causal connection. Future work might explore a more coherent formalization of causal connectedness in modal terms [46, 47].
Peirce introduces chain formation out of individual triadic cognitions as follows: “the
interpretant, or third, cannot stand in a mere dyadic relation to the object, but must stand in such
a relation to it as the [rst] representamen itself does. [...] The third must [...] be capable of
determining a third of its own. [...] All this must equally be true of the third’s thirds and so
on endlessly” [38]. For a conceptual analysis of typical research workows in computational
engineering, cf. Lenhard and Hasse [48, p. 73f.] as well as Lenhard and Ku¨ster [3, Section 2];
it is explained in previous work [
∧ TriadicCognition: ) → ∃( R˙ ∧ R˙ ∧ O ∧ O ) , where isGroundFor , denoted R¨ and subsumed under R cf. Fig. 1; for instance, could be a modelling step from which a molecular model for system is obtained as an interpretant, and could be a molecular simulation of system where the model is used to represent . There needs to be a ground10 that represents both and , ∀ (R¨ → R ).
In the present example, the ground for could be the assertion that “step epistemically grounds step by parameterizing the molecular model that is subsequently employed as a simulation input.” The reasoning according to which one cognitive step grounds another can itself be given the form of a sequence of cognitive steps; e.g., consider an explanation of how is epistemically grounded, providing a justication for a cognitive process where directly grounds . As in the example above, the grounds and then both represent . The preceding ground comes into existence before the new ground , such that is the sign and is the interpretant in a grounding interpretation⃗ ∀ ˓ →
→ ∃⃗ (R¨ ∧ R¨ ∧ ⃗3 ∧ Interpretation⃗: ) , ︁( ︁( ︁) ︁) ︁) (25) (26) (27) (28) (30) cf. Fig. 1. The representation relation R is reused in a grounding metonymization⃗ by which is assigned the grounded step as its new referent by ⃗3 . In general, ∀ ︁( ˓ → → ⃗∃ (R¨ ∧ ⃗3 ∧ Metonymization⃗: ) , ︁) cf. Fig. 1. Ultimately, a triadic cognition is grounded epistemically if there is an accepted presupposition that logicallyPrecedes it (denoted ˓→+) directly or indirectly ∀ ︁( (︀ Presupposition: ∨ ∃⊥(˓→+⊥ ∧ Presupposition:⊥)︀) ↔ GroundedCognition: )︀ ∧ (GroundedCognition: → Cognition: ) ∧ (Presupposition: → CognitiveStep: ) , (29) where ˓→+ is the transitive closure of ˓→ ∀ (︀ ˓→+ ↔
︀( ∃ (˓→+ ∧ ˓→ ) ∨ ˓→ )︀ .
10To Peirce [38], a ground is “an idea” that explains how a sign relates to an object. The present use of the
term applies this specically to an explanation that provides epistemic grounding to a cognition, as understood by
Williams: “Epistemic grounding is a matter of reliability. A belief is epistemically grounded [... if and only if] it is
formed via a process that in fact makes it likely to be true” [
Relations from domain ontologies, which are comparably specic, oen correspond to chains of top-level relations, which are more generic; as Zhou et al. [51] put it, they can be “used to ‘atten’ the structure of the other ontology by short-cutting a property chain.” Since the OWL description logic ℛℐ only permits one-way chain inclusions [52], in what is usually the wrong direction to implement the alignment, it can be useful if constructs for chains out of generic relations are explicitly included in a foundational or mid-level ontology to facilitate an alignment. Here, these abstract relations are P˙ (isProperPartOf), R (isRepresentamenFor), and their inverse relations. Accordingly, the PIMS-II mid-level ontology includes the mereosemiotic chain relations that were introduced in previous work when the VIMMP domain ontologies were aligned with the EMMO; these relations were found to be helpful or even necessary in many cases [18, Chapter 5]. The present system of chain relations is thus constituted by the free monoid M⋆ over M = { P˙, P˙− , R, R− }, with identity as the neutral element.11 For any Q, Q′ ∈ M⋆ ∀ (︀ ∃(Q ∧ Q′) ↔
QQ′)︀ , and inverse chains are obtained by (QQ′)− ≡ (Q′)− Q− , i.e., for any Q1, ..., Q ∈ M ∀(Q1 · · ·
Q ↔
Q− · · ·
Q1− ).
As a consequence of the strong mereotopology from Section 2.2, an implementation of the mereosemiotic chain relations can disregard many combinations of elements that are equivalent 11For the OWL implementation, the following naming convention is employed: The binary product relations are called overlapsWith ( P˙− P˙), sharesReferentWith (RR− ), and sharesRepresentamenWith (R− R). The names for higher-order product relations begin with the prex ms (for “mereosemiotics”), followed by the elements IP for “is proper part of,” HP for “has proper part,” IR for “is representamen for,” and HR for “has representamen.” In this way, e.g., the name msIPHRHPIP is used for the product P˙R− P˙− P˙. (31) (32) or redundant. For Q, Q′ ∈ M⋆, it follows from Axioms (4), (6), and (31) that ∀(Q P˙2Q′ ↔
Q P˙Q′), so that chains containing the factor P˙2 need not be considered; the same applies to P˙− 2. Similarly, any chains containing the “underlap” factor P˙ P˙− can be eliminated by ∀ ︁(
Q P˙ P˙− Q′ ↔ (∃′ Q′ ∧ ∃′ Q′′) , ︁) where Q, Q′ ∈ M⋆, since P˙ P˙− ≡ ⊤
Q, cf. Section 2.2; therefore, any elementary proposition on Q P˙ P˙− Q′ can be replaced with a conjunction over two separate existential propositions on Q include an explicit declaration of Q P˙ P˙− Q′ in the ontology. By construction and Q′ (which remain expressible in ℛℐ description logic) so that it is not necessary to ∀(Q1Q2Q3 →
Q1Q2Q2− Q2Q3), for all Q1, Q2, Q3 ∈ M⋆, and from mereotopology ∀(QQ′ →
Q P˙− P˙Q′), ∀(Q P˙Q′ →
Q P˙− P˙Q′) ∧ ∀(Q P˙− Q′ →
Q P˙− P˙Q′), yielding a dense hierarchy of relational subsumptions over M⋆, cf. Fig. 2. for any Q, Q′ ∈ M⋆, since P˙− P˙ is reexive and P˙ and P˙− are subrelations of P˙− P˙, cf. Section 2.2,
The present ontology permits the application of modal operators a) to relations, by which necessary and possible relations □ Q and ♢ Q can be constructed from a relation Q, and b) to rules, yielding laws as rules of the type □ (
→ ), where and are propositions. Beside qualied modal operators □ and ♢ , which require a descriptor of the applicable modal context , it includes absolute necessity and possibility □ and ♢ , which are free of context. The absolute operators satisfy the S5 axioms of modal logic □
□ ( → ) ⇒ ⇒ ⇒ ♢□ ( (□ , ∧ □
),
→ □ ),
where and are propositions. Motivated by the construction from Section 2.1, where the
domain is necessarily (understood here as absolute necessity), necessitism is applied; i.e.,
the existence of an object is a matter of absolute necessity [
⇒ ∃x ♢ .
All existing objects exist necessarily because they are here dened as spatiotemporal entities and the spatiotemporal extension of the domain is regarded as an absolute necessity; contingency is thereby shied to the relations between objects. This does not mean that counterfactual propositions need to be absolutely impossible, or that it becomes impossible to speak of contingent phenomena – quite the opposite: This construction is introduced here precisely to solve the paradox that contingent situations (including multiple mutually contradictory scenarios, as in an optimization) can occur as referents in actually occurring cognitive processes [25, Section 3.2]. In such cases, it is safe to say that, e.g., a model of an undesirable event , with the representation relation R, does retain an actually existing referent even if we hope or assume that the event as such will not occur; the spatiotemporal existence of is nonetheless a necessity.
By the same line of reasoning, mereotopological essentialism is supported12 ∀ ((♢ C → □ C) ∧ (♢ ˓→t → □ ˓→t)) . (38) ≡ t, and for the instantiation of the mereotopologically dened concept Item, so that Analogous rules can then be deduced for all mereotopological relations, including P˙, ≤ ˙ , and ∀(♢ Item: → □ Item:).
The OWL implementation of PIMS-II [
The relation between absolute and qualied modes of necessity is not straightforward to characterize in general, and no such attempt is made in the present work. Multiple modal frameworks are a requirement for addressing problems such as those posed by McCarthy [58], or hypercontingency (“it may be possible” to construct a warp drive, but it may also be impossible) as discussed by Kaminski [59, p. 351f.]. Qualied necessity can go beyond absolute necessity; e.g., it was not absolutely necessary for Trump to lose reelection, but to a knowledge base that holds this information, it is epistemically necessary. On the other hand, qualied possibility can go beyond absolute possibility: If Jones and Lewis ℓ, who have never met before, will meet in the future and shake hands, their overall spacetime trajectories are connected, Cℓ, which is then absolutely necessary, □ Cℓ, due to mereotopological essentialism; however, since we do not know whether that will happen and are therefore unaware of the shape of and ℓ, appropriate use can be made of the qualied modal proposition ¬□ Cℓ in an adequate context.
Mereotopology includes the concept of a mereotopological collective, i.e., a spacetime object that is not connected as a whole and is decomposed into maximal connected components, its members, which are items and which are related to the associated collective by the relation ≤ ˙ (isMereotopologicalMemberOf), cf. Axiom (7). However, the practical use of this EMMO construction for annotating research data is far too limited to be sucient [25, Section 3.1]. Jones and Lewis ℓ from the example above (Section 4.2) might never meet during their lifetime: Then they are spatiotemporally disconnected from each other, ¬Cℓ, and their fusion (with ℓ ) has two members, ≤ ˙ and ≤ ˙ ℓ. Or they might meet and shake hands, in which case their fusion becomes one item. We do not know which is the case, and if we did, it would still require us to handle dierent pairs of people dierently depending on irrelevant circumstantial phenomena.
A viable ontology that deals with research data requires additional kinds of collectives. Here, in line with the general structure of the present approach, SemioticCollective individuals (to which their members are related by ≤ ¨ , isSemioticMemberOf) are introduced to complement the MereotopologicalCollective individuals (objects of the relation ≤ ˙ ) such that generally, Collective individuals (objects of ≤ ) have at least two members
∀ (∃ ≤ → ∃(≤ ∧ ≤ ∧ ̸= )) , ∀ (︀ (≤ ˙ ∨ ≤ ¨ ) → ≤ )︀ ∧ ∀(≤ → P˙), (39) (40) whereby membership is subsumed under proper parthood. It is common to classify collectives into dierent kinds depending on how their components or members interact or are assembled into a whole; e.g., Masolo et al. [60] propose three types: Pluralities like “Alice and Bob,” proper collectives (e.g., forests or organizations), and composites “that have another sort of internal structure” [60]. Canavotto and Giordani [61] distinguish between heaplike and non-heaplike collectives, e.g., contrasting “a bunch of puzzle pieces” (heaplike) against “one puzzle made of those pieces” [61]. Semiotic collectives are characterized by joint action as a representational element, i.e., as a referent or representamen; PIMS-II distinguishes the following four kinds of semiotic collectives: 1. In a Plurality , the members (with ◁p) appear together as one representational element, all contributing to this eect in the same way; the members of a plurality can be anything other than another plurality or a structure. 2. In a Structure , the members (with ≺ ) constitute one representational element, but all in dierent roles; anything except structures can be a member of a structure.13 3. In an Articulation , to which its members are related by ◁r (“ realizes ”), dierent realizations of a single representational element are grouped together; e.g., copies of the same data item on dierent computers, multiple ways of denoting or encoding the same molecular model, or spoken utterances and written versions of the Lord’s Prayer in dierent languages can be grouped together into articulations. The realizations (members) of an articulation cannot include any semiotic collectives. 4. A Proposition has articulations as its members, denoted ◁a (“ articulates ”); this construction is to be employed whenever there are several ways in which the same propositional content was expressed and it is this shared semantic and/or pragmatic content that is relevant, rather than the exact way in which it was stated.
Following the paradigm of semiotic monism, no distinction is made between collectives that appear as a referent or a representamen. Membership is further generalized to constitutivity (denoted ¨C), cf. Axiom (23), which requires spatiotemporal overlap, and to underlying (denoted ¨C+), the transitive closure of ¨C, which is antireexive
∀(≤ → ¨C) ∧ ∀(¨C → P˙− P˙), ∀ (︁ ¨C+ ↔ (∃(¨C+ ∧ ¨C) ∨ ¨C)︁) ∧ ¬∃ ¨C+; (41) (42) e.g., the articulations “200” and “kPa” are constitutive of the articulation “200 kPa.” This relation cannot be subsumed under proper parthood, since realizations of the same articulation “200” are proper parts of realizations of other articulations, such as “200 K,” that are disjoint with “200 kPa.” It is le open whether constitutivity is reducible to a construction involving modal relations; work by Vogt [62] suggests that this is challenging, since there are many ways in which one object may be constitutive of another.
Arndt et al. observe that it is “very common for standardization bodies on all levels (regional,
super-regional, international) oen to provide an inconsistent, ambiguous set of concepts,
13Pluralities are permitted as members of structures, to be employed as follows: If and contribute to the
appearance of a structure as a referent or a representamen in the same way, while contributes in a dierent way,
the structure has two members. First, the plurality of and ; second, .
terms, and denitions. This is especially true for subjects that are relevant in a wide range of
domains” [63]. Ontology-based data technology aims at improving consistency, and facilitating
a uniform understanding of basic cross-domain concepts is a task that is usually attributed
to foundational ontologies. To achieve this goal, it is necessary to provide a formalization
of the underlying ontological paradigm, going beyond description logic which is insucient
to express many typical axioms. Mereotopology in combination with Peircean semiotics, or
mereosemiotics, is an ontological paradigm that is already in use by one foundational ontology
(EMMO [
Despite the uptake of this ontological paradigm in data management practice, there is little literature so far on the interaction between spatiotemporal parthood/connectedness on the one hand and cognitive processes consisting of Peircean triads on the other hand; none, to the knowledge of the author, includes an axiomatization comparable to that of the paradigms underlying other foundational ontologies. Addressing this challenge, the axiomatization of the core parts of PIMS-II in modal rst-order logic, given in the present work,14 provides mereosemiotics with an unambiguous formalization. While the present axiomatization does not entail four-dimensionalism, it is consistent with it; thereby, it species a coherent approach to integrating semiotics with four-dimensionalism and nominalism (strongly rejected by Peirce, but enforced by the EMMO). By this approach, research data provenance can be denoted in terms of cognitive processes, e.g., experimental procedures or simulation workows, documenting the reliability and supporting the FAIRness of data that are made available on research data infrastructures.
Supplementary information is made openly accessible through Zenodo [
This work was funded by the German Research Foundation (DFG) through the National Research Data Infrastructure for Catalysis-Related Sciences (NFDI4Cat), DFG project no. 441926934, within the National Research Data Infrastructure (NFDI) programme of the Joint Science Conference (GWK). It was facilitated by activities of the Innovation Centre for Process Data Technology (Inprodat e.V.), Kaiserslautern, Germany. Discussions in the Metadata4Ing group within NFDI4Ing, DFG project no. 442146713, are acknowledged.
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The following PIMS-II concepts are directly relevant to this work: • Articulation: A semiotic collective such that ∃ ◁r. the realizations of a single articulation can include literal (written or digital) and non-literal (e.g., spoken) versions; taxonomy: Articulation ⊑ SemioticCollective. • Cognition: Process in which signs represent objects; taxonomy: Cognition ⊑ Process. • CognitiveStep: Elementary cognition (e.g., a triad); taxonomy: CognitiveStep ⊑ Cognition. • Collective: Anything that has members (an with ∃ ≤ ); taxonomy: Collective ⊑ Object. • GroundedCognition: Cognition that is logically preceded by a Presupposition, cf. Axiom (29); taxonomy: GroundedCognition ⊑ Cognition. • Interpretation: Semiosis that does not require the object to participate and be present physically; taxonomy: Interpretation ⊑ Semiosis. • Item: Connected component of spacetime, cf. Axiom (8); taxonomy: Item ⊑ Object. • MereotopologicalCollective: Anything that is not an Item, i.e., any such that ∃ ≤ ˙ ; taxonomy: MereotopologicalCollective ⊑ Collective. • Metonymization: Semantic change that satises Axiom (22) such that there is a “real causal connection” [40, p. 142], C˙⋆′, between the old referent and the new referent ′; taxonomy: Metonymization ⊑ SemanticChange. • Object: All that exists is an Object. • Perception: Semiosis that requires the object to participate and be present physically, cf. Axiom (20); taxonomy: Perception ⊑ Semiosis. • Plurality: A semiotic collective such that ∃ ◁p. Members of a plurality engage in representation jointly, all in the same way or role; taxonomy: Plurality ⊑ SemioticCollective. • Presupposition: Anchor point for epistemic grounding – some previous cognitive step that is not subject to further scrutiny; taxonomy: Presupposition ⊑ CognitiveStep. • Process: Connected region (Item) in which one or multiple objects participate (have a role), i.e., any such that ∃ ¨P is a Process, cf. Axiom (16); taxonomy: Process ⊑ Item. • Proposition: A semiotic collective such that ∃ ◁a . The members of a proposition are articulations that express some joint semantic and/or pragmatic content, namely ; taxonomy: Proposition ⊑ SemioticCollective. • SemanticChange: Cognitive step with the structure old referent – sign – new referent as in Axiom (21), cf. Paradis [45]; taxonomy: SemanticChange ⊑ TriadicCognition. • Semiosis: Cognitive step with the structure sign – object – interpretant following Peirce [38], cf. Axiom (19); taxonomy: Semiosis ⊑ TriadicCognition. • SemioticCollective: An with ∃ ≤ ¨ , i.e., a collective that acts jointly as a representational element (i.e., representamen or referent); taxonomy: SemioticCollective ⊑ Collective. • Structure: A semiotic collective such that ∃ ≺ . The members of a structure engage in representation together, but all contributing in dierent ways or roles; taxonomy: Structure ⊑ SemioticCollective. • TriadicCognition: Cognitive step that is constituted by the interaction between three elements, i.e., any such that ∃123 3 123; taxonomy: TriadicCognition ⊑ CognitiveStep.
The following PIMS-II relations are directly relevant to this work: symbol hierarchy isSpatiotemporallyDisconnectedFrom isTemporallyConnectedWith isTemporallyIncludedIn isThirdElementIn isTriadOf logicallyPrecedes realizes sharesReferentWith sharesRepresentamenWith temporallyCoextendsWith temporallyPrecedes temporallyOverlapsWith overlapsWith underlies ⊤Q
C ¬C → ⊤Q C P˙− P˙ (For descriptions cf. http://www.molmod.info/semantics/pims-ii.ttl.) (relates a TriadicCognition to an rdf:List)