In this short paper we describe COCOS, a tool we are currently developing in order to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. COCOS is based on a probabilistic extension of the logic of typicality ALC + TR by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”) and it embeds a set of cognitive heuristics for concept combination.
Inventing novel concepts by combining the typical knowledge of pre-existing ones is an
important human creative ability. Dealing with this problem requires, from an AI
perspective, the harmonization of two conflicting requirements that are hardly
accommodated in symbolic systems: the need of a syntactic compositionality (typical of logical
systems) and that one concerning the exhibition of typicality effects [
In this paper we describe our work in progress in this field of research. We describe
COCOS, a software system able to account for this type of human-like concept
combination. COCOS relies on a nonmonotonic Description Logic (DL) of typicality called
TCL (typical compositional logic) recently introduced in [
As a second ingredient, we consider a distributed semantics similar to the one of
probabilistic DLs known as DISPONTE [
The proposed system COCOS is able to tackle the problem of composing
prototypical concepts. As an additional element we employ a method inspired by cognitive
semantics [
The current version of the system is implemented in Pyhton and exploits the translation
of an ALC + TR knowledge base into standard ALC introduced in [
Our system relies on the procedures developed for logic TCL. More in detail, we consider a KB K = hR; T ; Ai where R is a finite set of rigid properties of the form C v D, T is a finite set of typicality properties of the form
p :: T(C) v D
where p 2 (0:5; 1) R is the probability of the typicality inclusion and A is the ABox, i.e. a finite set of formulas of the form either C(a) or R(a; b), where a and b are individual names, C is a concept and R is a role.
Given two concepts CH and CM occurring in K, the logic TCL allows one to define the compound concept C as the combination of the HEAD CH and the MODIFIER CM , where C v CH u CM and the typical properties of the form T(C) v D to ascribe to the concept C are obtained by selecting suitable scenarios. Intuitively, a scenario is a knowledge base obtained by adding to all rigid properties in R and to all ABox facts in A only some typicality properties coming from either the HEAD or the MODIFIER. Each scenario is equipped by a probability defined as p1 : : : pi (1 q1) : : : (1 qj ), where p1 :: T(E1) v F1; : : : ; pi :: T(Ei) v Fi are the typicalities included in the scenario, whereas q1 :: T(G1) v H1; : : : ; qj :: T(Gj ) v Hj are those not included in the scenario.
Intuitively, the selected scenarios are those satisfying the following properties: 1. are consistent with respect to K; 2. are not trivial, in the sense that the scenarios considering all properties that can be consistently ascribed to C are discarded; 3. are those giving preference to the typical properties of the HEAD CH (with respect to those of the MODIFIER CM ). Notice that, in case of conflicting properties like D and :D, given two scenarios w1 and w2 such that an inclusion p1 :: T(CH ) v D belongs to w1 whereas p2 :: T(CM ) v :D belongs to w2, the scenario w2 is discarded in favor of w1.
In order to select the wanted scenarios, COCOS applies points 1, 2, and 3 above to blocks of scenarios with the same probability, in decreasing order starting from the highest one. More in detail, COCOS first discards all the inconsistent scenarios, then it considers the remaining (consistent) ones in decreasing order by their probabilities. It then considers the blocks of scenarios with the same probability as follows: – it discards scenarios considered as trivial, consistently inheriting all (or most of) the properties from the starting concepts to be combined; – among the remaining ones, it discards those inheriting properties from the MODIFIER in conflict with properties inherited from the HEAD in another scenario of the same block (i.e., with the same probability); – 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, COCOS repeats the procedure by considering the block of scenarios, all having the immediately lower probability.
The knowledge base obtained as the result of combining concepts CH and CM into the compound concept C is called C-revised knowledge base:
KC = hR; T [ fp : T(C) v Dg; Ai; for all D such that T(C) v D is entailed in all the scenarios selected by COCOS. Notice that, since the C-revised knowledge base is still in the language of the TCL logic, we can iteratively repeat the same procedure in order to combine not only atomic concepts, but also compound concepts.
Some pictures of COCOS are shown in Figure 2. An example of the application of COCOS for the generation of a new concept is shown in the next concluding section. 3
We exploit the system COCOS as a creative support tool to generate a new type of character in the field of computational creativity for a video game or a movie.
Let us assume to generate a novel concept obtained as the combination of concepts Villain (as HEAD) and Chair (as MODIFIER). Let K = hR; T ; ;i be as follows:
and T is as follows:
T5 0:95 :: T(Chair ) v :Animate
We consider the 512 scenarios that can be generated from nine typicality inclusions T1– T9, from which we discard the inconsistent ones, namely those including T5: indeed, since R2 imposes that villains are animate, in the underlying ALC + TR we conclude that Villain u Chair v Animate , therefore all scenarios including T5, imposing that Villain u Chair v :Animate are inconsistent. We also discard the most obvious scenario including all the typicality inclusions of T , having probability of 14%. Among the remaining scenarios, the most probable contains all the inclusions related to the HEAD, namely T1, T2, T3, and T4, whereas it contains T6, T8, and T9 concerning the MODIFIER. This scenario is the preferred one from a cognitive point of view. However, in this application setting, we could imagine to use our framework as a creativity support tool and thus considering alternative - more surprising - scenarios by adding additional constraints. For example, by imposing that the compound concept should inherit six properties, we would get that the scenario having the highest probability (3:2%) is the one including all the properties of the HEAD, namely T1, T2, T3 and T4, and two out of four properties of the MODIFIER, namely T6 and T8, Similarly, we could decide to prefer - still more surprising - scenarios, by selecting those with probability of 2:51%, obtaining the following, plausible but not obvious, creative definitions of villain chair: