In this work we continue our investigation on tools for the dynamic generation of novel knowledge by exploiting a recently introduced extension of a Description Logic of typicality able to combine prototypical descriptions of concepts. Given a goal expressed as a set of properties, in case an intelligent agent cannot find a concept in its initial knowledge base able to fulfill all these properties, our system exploits the Description LogicTCL in order to find two concepts whose creative combination satisfies the goal. The knowledge base of the agent is then extended by the prototype resulting from the concept combination, and the combined concept represents the solution for the initial goal. In addition, we show how the tool we propose can be employed in the field of cognitive architectures in order to overcome situations like theimpasse in SOAR by extending the possible options of its subgoaling procedures.
CEUR ceur-ws.org
https://docenti.unisa.it/024406/home (A. Lieto); https://www.di.unito.it/~pozzato (G. L. Pozzato)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). it is served chilled). Both cofee and Limoncello are after meal drinks. Cold winters in Turin suggest to have a hot after-meal drink, also being sweet and having taste of milk. None of the concepts in the knowledge base of the agent are able to achieve the goal on their own, however, the combination between cofee and chocolate with cream provides a solution.
In this paper we introduce EDIFICA, which stands for “ExtenDIble & FlexIble concept Combination Architecture”, a tool extending GOCCIOLA [3] following this approach in the context of Description Logics (from now on, DLs for short). DLs are one of the most important formalisms of knowledge representation and are at the base of the languages for building ontologies such as OWL. In this respect, we exploit the Description LogicTCL, recently introduced in order to account for the phenomenon of concept combination of prototypical concepts [ 6]. The logic TCL relies on the logic of typicality ℒ + TRRaCl [7], whose semantics is based on the notion of rational closure, as well as on the DISPONTE semantics of probabilistic DLs [8], and is equipped with a cognitive heuristic used by humans for concept composition. In this logic, typicality inclusions of the form ∶∶ T() ⊑ are used to formalize that “we believe with degree about the fact that typical s are s”. As in the distributed semantics, this allows us to consider diferent scenarios containing only some typicality inclusions, each one having a suitable probability. Such scenarios are then used to ascribe typical properties to a concept obtained as the combination of two concepts, revising the initial knowledge base with the addition of typical properties of . In the example, the revised knowledge base provided by the logic TCL contains typical properties of the combination of cofee and chocolate with cream, which suggests to consider a beverage corresponding to the famous Turin drink known as Bicerín (little glass), made by cofee, chocolate and cream.
EDIFICA tries to tackle the main criticisms and drawbacks of GOCCIOLA, namely: • GOCCIOLA randomly selects concepts to be combined; as an alternative, EDIFICA selects such candidates starting from the properties of the goal to be fullfilled; • GOCCIOLA is able to combine only two concepts at a time, whereas EDIFICA has no longer this limitation; • EDIFICA implements a more sophisticated mechanism in order to choose the list of concepts to be combined among all the candidates; • EDIFICA adopts a “smart” mechanism in generating scenarios in the logic TCL, for instance by discarding inconsistent ones, rather than generating all of them by means of a “brute force” mechanism as in GOCCIOLA.
Moreover, EDIFICA ofers an open and modular architecture, that allows the user to provide and add specific and suitable mechanisms. In addition, we also show how the proposed tool can be employed in the field of cognitive architectures in order to overcome situations like the impasse in the well-established architecture SOAR [9] by extending the possible options of its subgoaling procedures.
The plan of the paper is as follows. In Section 2 we briefly recall the DL for concept combination TCL. In Section 3 we provide a formal description of the problem of dynamic knowledge generation in the context of the logicTCL. In Section 4 we recall the main features of the ancestor of EDIFICA, namely the system GOCCIOLA, and we show that it is a promising candidate to tackle such a problem by means of some paradigmatic examples. In Section 5 we describe the novel system EDIFICA, by emphasizing how it improves the existing GOCCIOLA. In Section 6 we show how EDIFICA can be employed in the field of cognitive architectures by extending the options of their subgoaling procedures. We conclude in Section7 with some pointers to future issues.
In [6] we have introduced a nonmonotonic Description Logic of typicality calledTCL (typicalitybased compositional logic). This logic combines two main ingredients. The first one relies on the DL of typicality ℒ + TRRaCl introduced in [7], which allows to describe theprotoype of a concept. In this logic, “typical” properties can be directly specified by means of a “typicality” operator T enriching the underlying DL, and a TBox can contain inclusions of the formT() ⊑ to represent that “typical s are also ”. As a diference with standard DLs, in the logic ℒ + TRRaCl one can consistently express exceptions and reason about defeasible inheritance as well. For instance, a knowledge base can consistently express that “normally, athletes are fit”, whereas “sumo wrestlers usually are not fit” by T(Athlete) ⊑ Fit and T(SumoWrestler ) ⊑ ¬Fit, given that SumoWreslter ⊑ Athlete. The semantics of the T operator is characterized by the properties of rational logic[10], recognized as the core properties of nonmonotonic reasoning. ℒ + TRRaCl is characterized by a minimal model semantics corresponding to an extension to DLs of a notion of rational closureas defined in [ 10] for propositional logic: the idea is to adopt a preference relation among ℒ + TRRaCl models, where intuitively a model is preferred to another one if it contains less exceptional elements, as well as a notion ofminimal entailment restricted to models that are minimal with respect to such preference relation. As a consequence, T inherits well-established properties likespecificity and irrelevance: in the example, the logic ℒ + TRRaCl allows us to infer T(Athlete ⊓ Bald) ⊑ Fit (being bald is irrelevant with respect to being fit) and, if one knows that Hiroyuki is a typical sumo wrestler, to infer that he is not fit, giving preference to the most specific information.
As a second ingredient, we have considered a distributed semantics similar to the one of
probabilistic DLs known as DISPONTE [8], allowing to label inclusions T() ⊑ with a real
number between 0.5 and 1, representing its degree of belief/probability. In a slight extension
of the above example, we can express a degree of belief in the typicality inclusions about
athletes and sumo wrestlers: we believe with a probability of 80% that, normally, athletes
are fit whereas sumo wrestlers are not; furthermore, we believe that athletes are usually
young with a higher degree of95%. This is formalized by the following knowledge base: (
The logic TCL seems to be a promising candidate in order to tackle the problem of concept combination. Combining the typical knowledge of pre-existing concepts is among the most creative cognitive abilities exhibited by humans. This generative phenomenon highlights some crucial aspects of the knowledge processing capabilities in human cognition and concerns high-level capacities associated to creative thinking and problem solving. Dealing with this problem requires, from an AI perspective, the harmonization of two conflicting requirements that are hardly accommodated in symbolic systems (including formal ontologies [ 11]): the need for a syntactic and semantic compositionality (typical of logical systems) and that one concerning the exhibition of typicality efects. According to a well-known argument [ 12], in fact, prototypes are not compositional. The argument runs as follows: consider a concept like pet fish . It results from the composition of the concept pet and of the concept fish . However, the prototype of pet fish cannot result from the composition of the prototypes of a pet and a fish: e.g. a typical pet is furry and warm, a typical fish is grayish, but a typical pet fish is neither furry and warm nor grayish (typically, it is red).
Given a knowledge base = ⟨ℛ, , ⟩ , where ℛ is the set of standard (rigid) inclusions of ℒ , is the set of typicality inclusions, and is the ABox, and given two concepts and occurring in , the logic TCL allows defining a prototype of the compound concept as the combination of the HEAD , the dominant element in the combination, and the MODIFIER . Typical properties to ascribe to the combination of and are inclusions of the form T() ⊑ (or, equivalently, T( ⊓ ) ⊑ ), whose intuitive meaning is that “ is a typical property of combining and ”, and are obtained by considering blocks of scenarios with the same probability, in decreasing order starting from the highest one. We first discard all the inconsistent scenarios, then: • we discard those scenarios considered astrivial, consistently inheriting all the properties from the HEAD from the starting concepts to be combined. This choice is motivated by the challenges provided by task of common-sense conceptual combination itself: in order to generate plausible and creative compounds it is necessary to maintain a level of surprise in the combination. Thus both scenarios inheriting all the properties of the two concepts and all the properties of the HEAD are discarded since prevent this surprise; • among the remaining ones, we discard those scenarios inheriting properties from the
MODIFIER in conflict with properties that could be consistently inherited from the HEAD; • if the set of scenarios of the current block is empty, i.e. all the scenarios have been discarded either because trivial or because preferring the MODIFIER, we repeat the procedure by considering the block of scenarios having the immediately lower probability. Remaining scenarios are those selected by the logicTCL. The ultimate output of our mechanism is a knowledge base in the logicTCL whose set of typicality properties is enriched by those of the compound concept . Given a scenario satisfying the above properties, we define the properties of as the set of inclusions ∶∶ T() ⊑ , for all T() ⊑ that are entailed from in the logic TCL. The probability is such that: • if T( ) ⊑ is entailed from , that is to say is a property inherited either from the HEAD (or from both the HEAD and the MODIFIER), then corresponds to the degree of belief of such inclusion of the HEAD in the initial knowledge base, i.e.∶ T( ) ⊑ ∈ ; • otherwise, i.e. T( ) ⊑ is entailed from , then corresponds to the degree of belief of such inclusion of a MODIFIER in the initial knowledge base, i.e. ∶ T( ) ⊑ ∈ . The knowledge base obtained as the result of combining concepts and into the compound concept is called -revised knowledge base, and it is defined as follows: = ⟨ℛ, ∪ { ∶
T() ⊑ }, ⟩, for all such that either T( ) ⊑ is entailed in or T( ) ⊑ is entailed in , and is defined as above. In [6] we have shown that reasoning in the logicTCL remains in the same complexity class of standard ℒ Description Logics, namely that reasoning in TCL is ExpTime-complete.
We exploit the logic TCL in order to tackle the following problem: given a knowledge base in the Description LogicTCL, an intelligent agent has to achieve a goal intended as a set of concepts { 1, 2, … , }. More precisely, the agent has to find a solution for the goal, namely a concept such that, for all properties , it holds that either ⊧ ⊑ or ⊧ T() ⊑ in the logic of typicality ℒ + TRRaCl . If does not contain any solution for the goal, then the agent tries to generate a new concept by combining two existing ones 1 and 2 by means of the logic TCL: is then considered a solution for the goal if, considering the( 1 ⊓ 2)-revised knowledge base extending , we have that, for all properties , it holds that either ⊧ ⊑ or ⊧ T() ⊑ in the logic of typicality ℒ + TRRaCl .
This is formally defined as follows: Definition 1. Given a knowledge base in the logic TCL, let be a set of atomic concepts { 1, 2, … , } calledgoal. We say that a concept is a solution to the goal if either: • for all ∈ , either ⊧ ⊑ or ⊧
T() ⊑ in the logic TCL or • corresponds to the combination of two concepts 1 and 2 occurring in , i.e. ≡ 1 ⊓ 2, and the -revised knowledge base provided by the logic TCL is such that, for all ∈ , either ⊧ ⊑ or ⊧ T() ⊑ in the logic TCL.
Let us conclude this section by formalizing the example of the Introduction.
Example 2. In the example of the Introduction, suppose that contains the information that, normally, cofee contains cafeine and is a hot beverage; moreover, we have that the chocolate with cream is normally sweet and has a taste of milk, whereas Limoncello is not a hot beverage (normally, it is served chilled). Both cofee and Limoncello are after meal drinks. We can represent these information as follows: 0.9 ∶∶ T(Cofee ) ⊑ AfterMealDrink 0.8 ∶∶ T(Cofee ) ⊑ WithCafeine 0.85 ∶∶ T(Cofee ) ⊑ HotBeverage Limoncello ⊑ AfterMealDrink 0.9 ∶∶ T(Limoncello) ⊑ ¬HotBeverage 0.65 ∶∶ T(ChocolateWithCream) ⊑ Sweet 0.95 ∶∶ T(ChocolateWithCream) ⊑ TasteOfMilk Cold winters in Turin suggest to have a hot after-meal drink, also being sweet and having taste of milk. We can then define a goal as
= { AfterMealDrink , HotBeverage, Sweet, TasteOfMilk}.
None of the concepts in the knowledge base represent a solution for the problem. However, the combination between the concepts Cofee and ChocolateWithCream represents a solution. Indeed, the revised knowledge base obtained by exploiting the logicTCL to combine these concepts allows the agent to extend its knowledge with the following typicality inclusions: 0.9 ∶∶ T(Cofee ⊓ ChocolateWithCream) ⊑ AfterMealDrink 0.85 ∶∶ T(Cofee ⊓ ChocolateWithCream) ⊑ HotBeverage 0.65 ∶∶ T(Cofee ⊓ ChocolateWithCream) ⊑ Sweet 0.95 ∶∶ T(Cofee ⊓ ChocolateWithCream) ⊑ TasteOfMilk providing a solution for the goal corresponding to the famous Turin drink known asBicerín (little glass).
In this Section we describe GOCCIOLA, a preliminary implementation of a system able to extend the knowledge of an agent in order to fulfill a set of properties representing the goal that the agent wants to achieve. GOCCIOLA is implemented in Python and its current version, along with the files for the examples presented in this paper, are available at http://di.unito.it/gocciola. The architecture of the system GOCCIOLA is shown in Figure1.
As an example, let us consider the goal: object, cutting, graspable, in other words our agent is looking for an object being graspable and which is able to cut. The initial knowledge base is formalized in the language of the logic TCL and it is stored in a suitable file. Rigid properties, holding for all individuals of a given class, are stored as pairs object-property, whereas typical properties are formalized as triples object-property-probability. We have considered an extension with probabilities of a portion of the ontologyopencyc1. As an example, the concept Vase is stored as follows (on the right the corresponding knowledge base inTCL): 1https://github.com/asanchez75/opencyc .
To run GOCCIOLA, the user has to invoke the Python interpreter on the file main.py, which consults the initial knowledge base and the goal to achieve (classesReadKnowledgeBaseand Goal, respectively). First of all, the method resolve_goalchecks whether the knowledge base contains a concept immediately satisfying it, i.e. exhibiting all the concepts of the goal either as rigid or typical properties: in this case, the system is done, and GOCCIOLA ends its computation by suggesting such a concept as the solution. In case does not exist, the system GOCCIOLA tries to extend the knowledge base of the agent by looking for at least two concepts, 1 and 2, whose combination via TCL generates a concept ′ satisfying the goal. More in detail: • GOCCIOLA computes a list of concepts of the initial knowledge base satisfying at least a property of the goal. As an example, suppose that the following inclusions belong to the knowledge base:
Spoon ⊑ Graspable 0.85 ∶∶ T(Spoon) ⊑ ¬Cutting 0.9 ∶∶ T(Vase) ⊑ Graspable
Vase ⊑ Object
Both Vase and Spoon are included in the list of candidate concepts to be combined; • for each item in the list of candidate concepts to be combined, GOCCIOLA computes a rank of the concept as the sum of the probabilities of the properties also belonging to the goal, assuming a score of 1 in case of a rigid property. In the example, Vase is ranked as 0.9 + 1 = 1.9, since both Graspable and Object are properties belonging to the goal: for the former we take the probability 0.9 of the typicality inclusion T(Vase) ⊑ Graspable, for the latter we provide a score of 1 since the property Vase ⊑ Object is rigid. Concerning the concept Spoon, GOCCIOLA computes a rank of 1: indeed, the only inclusion matching the goal is the rigid oneSpoon ⊑ Graspable; • GOCCIOLA checks whether the concept obtained by combining the two candidate concepts with the highest ranks, 1 and 2, is able to satisfy the initial goal. GOCCIOLA computes a double attempt, by considering first 1 as the HEAD and 2 as the MODIFIER and, in case of failure, 2 as the HEAD and 1 as the MODIFIER.
In order to combine the two candidate concepts 1 and 2, GOCCIOLA exploits the system CoCoS [13], a tool generating scenarios and choosing the selected one(s) according to the logic TCL. The current version of the system is implemented in Pyhton and exploits the translation of an ℒ + TRRaCl knowledge base into standard ℒ introduced in [14, 7] and adopted by the system RAT-OWL [15]. CoCoS makes use of the library owlready2 2 that allows one to rely on the services of eficient DL reasoners, e.g. the HermiT reasoner. GOCCIOLA also exploits WordNet sysnsets in order to extend its search space in case of a failure. In detail, if the goal contains properties not belonging to the initial knowledge base, GOCCIOLA looks for hypernyms or hyponyms in order to rewrite such properties.
As already mentioned in the Introduction, we have extended the system GOCCIOLA in order to tackle the main limitations afecting the systems, namely: • in order to achieve a given goal, GOCCIOLA randomly chooses concepts to be combined; • GOCCIOLA is able to deal only with combinations of two concepts at a time; • GOCCIOLA randomly chooses the two initial candidates to be combined in order to fulfill a goal; • in order to combine concepts 1 and 2, the underlying concept combination mechanism based on CoCoS [13] generates all 2 possible scenarios, where is the sum of the number of typicality inclusions of the form ∶∶ T( 1) ⊑ and the number of typicality inclusions of the form ∶∶ T( 2) ⊑ .
In this section we describe the main features of EDIFICA (https://github.com/JoddyJordan/ EDIFICA-Code) and we try to point out how it significantly improves both the performance and the results proposed by its ancestor GOCCIOLA.
The goal of EDIFICA is the same of GOCCIOLA: find a concept combination based on the generation of scenarios of possible properties able to achieve a given goal. The main diference 2https://pythonhosted.org/Owlready2/ is that EDIFICA is a tool born with an architecture that can be extended by the user. This architecture allows us to add a bunch of new features that are not present in GOCCIOLA. These new features are: • the possibility for the user to customize the input flows: information about rigid properties, information about typical properties and information about the goal to solve; • the possibility for the user to define a suitable module for the extraction of candidates for goal-resolution, in other words concepts to be combined for finding a solution for the initial problem; • the possibility for the user to define a chooser of the best candidate (i.e. a set of concepts) for the goal; • the possibility for the user to adopt a combination of an arbitrary number of concepts, with additional heuristics for the concept combination.
Furthermore, EDIFICA implements a more eficient scenario generation, in particular it implements a scheme of analysis of the properties involved in the concept combination in order to avoid the generation of inconsistent scenarios: in this way, not all2 scenarios are generated and – only later – discarded, they are simply not generated.
The open architecture of EDIFICA is shown in Figure2: such an architecture includes a set of interfaces, each expressing a function of the system; moreover, a user can add new interfaces, i.e. new functions, or re-define existing ones.
In order to better understand how EDIFICA improves GOCCIOLA, let us conclude this section by a running example. Suppose both the systems have the following knowledge base:
After this analysis, EDIFICA uses a recursive algorithm that fixes at every step the truth value for the choice of a specific typical property and updates the other typical properties by using the conflict and the coordination relations. In our example, only 6 scenarios are so generated, rather than 24 = 16. If each candidate scenario is inconsistent, EDIFICA will discard the candidate and pick the next list of concepts from the remaining ones.
We conclude this work by showing how the proposed system EDIFICA can integrate, and extend, the classical subgoaling mechanism embedded in a cognitive architecture like SOAR [9], with a particular reference to the impasse mechanisms developed in such architecture. In our opinion, this compliance represents an important aspect to point out since SOAR is one of the most mature cognitive architectures and has been used by many researchers worldwide during the last 30 years in the field of cognitive modelling and intelligent systems. This system was considered by Allen Newell a candidate for a Unified Theory of Cognition [ 16] and still represents an important pillar in the efort of building a general integrated model of cognition [ 17]. This system adheres strictly to Newell and Simon’s physical symbol system hypothesis [ 18] which states that symbolic processing is a necessary and suficient condition for intelligent behavior. One of the main themes in SOAR is that all cognitive tasks can be represented by problem spaces that are searched by production rules grouped into operators. These production rules are fired in parallel to produce reasoning cycles. From a representational perspective, SOAR exploits symbolic representations of knowledge (called chunks) and use pattern matching to select relevant knowledge elements. Basically, when a production rule matches the contents of declarative (working) memory, then the rule fires and the content from the declarative memory (called Semantic Memory in SOAR) is retrieved.
Such type of knowledge structures, however, are usually heavily used to perform standard logical reasoning and, as a consequence, are strongly biased towards a “classical” conceptualisation of knowledge in terms of necessary or suficient conditions and are not equipped with commonsense representational and reasoning knowledge components 3. If a problem (an impasse in SOAR terms) arises due to the fact that certain knowledge is lacking, resolving this impasse automatically becomes the new goal (and this process is known as subgoaling). This new goal becomes a subgoal of the original one, which means that once the subgoal is achieved, control is returned to the main goal. The subgoal has its own problem space, state and possible set of operators. Whenever the subgoal has been achieved it passes its results to the main goal, thereby resolving the impasse. Learning is keyed to the subgoaling process: whenever a subgoal has been achieved, new knowledge is added to the knowledge base to prevent the impasse that produced the subgoal from occurring again (this learning process is known as chunking). If an impasse occurs because the consequences of an operator are unknown, and in the subgoal these consequences are subsequently found, knowledge is added to SOAR‚Äôs memory about the consequences of that operator. An important feature in SOAR concerns the fact that it can also use external input as part of its impasse resolution process, therefore new knowledge can 3This problem arises despite the fact that the chunks in SOAR can be represented as a sort of frame-like structures containing some commonsense (e.g. prototypical) information. We remind to [ 19] for details analysis on such issue. extended the Semantic Memory of SOAR and can be incorporated into the learned rules. In this context, the proposed system can be integrated, and can extend, the SOAR subgoaling procedure as illustrated in Figure3. The process of bi-directional translation between a chunk-like representation and the language ofTCL can be provided as introduced in [20] and implemented in [ 15], where a typicality-based property is translated into a standard Description Logic knowledge base (corresponding to a chunk-based symbolic representation in SOAR). In particular, the overall approach is compliant with the idea of a goal-directed contextual activation of concepts obtained via a process of knowledge “proxyfication” [ 21] from the long-term memory to the short term memory of a cognitive agent (already employed in knowledge-based systems like DUAL-PECCS [22], integrated with diferent cognitive architectures, including SOAR [23, 24]). A final element emerging from the described compliance consists in the fact that that the output of the new subgoaling procedure (i.e. the novel concept dynamically generated in the KB and made available in the working memory of the architecture to solve the original goal) can be used in the SOAR learning mechanism known as chunking, which converts the obtained concept used to solve the goal at hand in the procedural memory of the system in order to avoid to perform ex-novo the same reasoning cycle in case the agent encouters againg the same goal to solve.
From a more implementative point of view, the above mentioned integration between the Semantic Memory in SOAR (SMEM) and our hybrid KB can be obtained as follows: SMEM is accessed through two dedicated working memory channels, called ^command and ^result. In particular, ^command is the branch of the working memory bufer where the GOAL setting takes places. In case the goal cannot be satisfied, this kind of request, instead of launching a standard search in the SOAR SMEM, can use our system to select which concepts can be potentially combined to extend the available knowledge and to solve the goal in hand. This kind of connection can be done by modifing the SOAR kernel and by creating novel RHS (Right Hand Side) functions able to launch our system, and its TCL knowledge base in order to take advantage of the reasoning procedure presented in the above sections. The result of this process will produce in output a novel prototype-based representation that is can be used to solve and goal. Such result can be stored in the ^result channel, the branch of the SOAR working memory bufer devoted to acquiring the output from the external modules. Once the result of our system is “proxyfied” and the goal is solved, it can then be used in the chunking mechanism of the architecture.
We have presented EDIFICA, a tool implementing a cognitive architecture whose aim is to dynamically extend a Description Logics knowledge base by exploiting conceptual combination. EDIFICA extends GOCCIOLA by trying to tckle its main criticisms, namely a random choice of the concepts to be combined in order to achieve a goal, a “brute force” approach in the generation of possible scenarios and the limitation to solutions obtained by combining only two concepts. Moreover, the architecture of EDIFICA is open and modular and can therefore easily be personalized by the user.
EDIFICA, as well as GOCCIOLA, relies on CoCoS, a tool for combining concepts in the logic TCL. In future research, we aim at studying the application of optimization techniques in [25, 26] in order to improve the eficiency of CoCoS and, as a consequence, of EDIFICA.
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