Abstract Our paper introduces an innovative automated system designed to extract logical rules using the $\textbf{T}^{\mathsf{\tiny CL}}$ logic from various datasets, with a particular emphasis on tabular data. Our starting point is the CN2 algorithm. Typically employed for classification tasks, we have adapted this algorithm to suit our descriptive objectives. We consider well-known datasets (such as Iris and Zoo) to illustrate our approach. Furthermore, we extend this analysis to a complex dataset, notably the GTZAN musical dataset. We have then tested our system by reclassifying the songs available in the GTZAN database with respect to the newly generated musical genres, obtaining encouraging results. This example showcases the algorithm’s efficacy in generating descriptive rules across different data domains. We discuss the adaptability of the proposed approach across various data types, including images, sounds and various heterogeneous structures.

Abstract In this paper we present our final solution to the problem of designing an efficient theorem prover for Conditional Logics with the selection function semantics. Conditional Logics recently have received a renewed attention and have found several applications in knowledge representation and artificial intelligence. In order to provide an efficient theorem prover for Conditional Logics, we introduce labelled sequent calculi for the logics characterized by well-established axioms systems including the axiom of strong centering CS, the axiom of conditional identity ID, the axiom of conditional modus ponens MP, as well as the conditional third excluded middle CEM, rejected by Lewis but endorsed by Stalnaker, as well as for the whole cube of extensions. The proposed calculi revise and improve the calculi SeqS introduced in Olivetti et al. (2007, ACM Trans. Comput. Logics, 8). We also present an implementation of these calculi in SWI Prolog, including a graphical interface in Python as well as standard heuristics and refinements that allow us to obtain an efficient theorem prover for the logics under consideration. Moreover, we present some statistics about the performances of the theorem prover, which are promising and significantly better than those of its predecessor CondLean, an implementation of the calculi SeqS.

Abstract In this paper we establish a link between fuzzy and preferential semantics for description logics and self-organizing maps (SOMs), which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalization. In particular, we show that the input/output behavior of a SOM after training can be described by a fuzzy description logic interpretation as well as by a preferential interpretation, based on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics. Properties of the network can be proven by model checking on the fuzzy or on the preferential interpretation. Starting from the fuzzy interpretation, we also provide a probabilistic account for this neural network model.

Reasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational closure. The rational closure has the merit of providing a simple and efficient approach for reasoning with exceptions, but it does not allow independent handling of the inheritance of different defeasible properties of concepts. In this work we outline a possible solution to this problem by introducing a weaker variant of the lexicographical closure, that we call skeptical closure, which requires to construct a single base. We develop a bi-preference semantics for defining a characterization of the skeptical closure.

We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic 𝒮𝒽𝒾𝓆. We provide a semantic characterization of rational closure in 𝒮𝒽𝒾𝓆 in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of 𝒮𝒽𝒾𝓆 into entailment in 𝒮𝒽𝒾𝓆. We discuss the extension of rational closure to more expressive description logics.

This special issue of Fundamenta Informaticae contains the revised, extended versions of selected papers presented at the Italian Conference on Computational Logic (Convegno Italiano di Logica Computazionale, CILC 2014) which was hosted by the University of Turin, Italy, from June 16th to June 18th, 2014.The event was the twenty-ninth edition of the annual meeting of the Italian Association for Logic Programming (GULP, Gruppo Ricercatori e Utenti di Logic Programming).Since its first edition, which took place in Genoa in 1986, the annual conference organized by GULP is the main occasion of meeting and exchanging ideas and experiences among Italian researchers who work in the field of Computational Logic.During the years, this annual meeting extended its horizons from the specific field of traditional Logic Programming to more general declarative programming as well as to Artificial Intelligence and Deductive Databases.All these areas had a very significant growth over the last decades and nowadays they all play a crucial role in the fields of Information Processing and Computer Science.The program of CILC 2014 included 29 technical papers accepted for presentation (23 for long presentation and 6 for short presentation).Paper selection was made by peer reviewing.The technical presentations were of high quality and concerned several topics related to computational logic, including probabilistic logic programming, verification of logic programs, answer set programming, revision and query of ontologies, argumentation theory, proof and decision systems for non-classical logics, computable set theory, multi-agent systems, and machine learning.The conference program included also two invited talks: (i) "From logic programming to argumentation and back", by Francesca Toni (Department of Computing, Imperial College London, U.K.), and (ii) "Tractable approaches to consistent query answering in ontology-based-data access", by Riccardo Rosati (DIAG, Dipartimento di Ingegneria informatica, automatica e gestionale, Università di Roma "Sapienza", Italy).Some of the papers presented at the conference were selected for this special issue and their authors were invited to submit an improved, extended version for publication.The papers that have been accepted went through a two-round careful review by qualified international referees, to whom we express our deep gratitude for their comments and criticisms.

The paper introduces a framework based on constructive conditional logics to define axiomatization, semantics and proof methods for access control logics. We formalize the well-known says operator as a conditional normal modality and, by considering some specific ombinations of access control axioms, we define four access control logics, namely, CondACLUC⁠, CondACLU4⁠, CondACLIC and CondACLI4⁠. Such logics integrate access control logics with intuitionistic conditional logics and provide a natural formulation of Boolean principals. The well-known 'speaks for' operator introduced in the logic ABLP is defined on the top of the says modality. We provide a Kripke model semantics for the logics and we prove that their axiomatization is sound and complete with respect to the semantics. Also, we develop sound, complete, cut-free sequent calculi for them. For the logic CondACLUC⁠, which (as concerns atomic principals) is slightly stronger than the logic ICL recently introduced by Garg and Abadi, we also provide a terminating sequent calculus, thus proving that the logic is decidable and that validity in CondACLUC is in PSPACE.

We propose a nonmonotonic extension of low complexity Description Logics EL ⊥ and DL-Litecore for reasoning about typicality and defeasible properties. The resulting logics are called EL ⊥ Tmin and DL-LitecTmin. we prove that entailment is in Π p 2 Concerning DL-LitecTmin,. With regard to EL ⊥ Tmin, we first show that entailment remains EXPTIME-hard. Next we consider the known fragment of Left Local EL ⊥ Tmin and we prove that the complexity of entailment drops to Π p 2. 1

We define an Intuitionistic Conditional Logic for Access Control called CICL. The logic CICLis based on a conditional language allowing principals to be defined as arbitrary formulas and it includes few uncontroversial axioms of access control logics. We provide an axiomatization and a Kripke model semantics for the logic CICL, and we prove that the axiomatization is sound and complete with respect to the semantics.

Extensions of Description Logics (DLs) to reason about typicality and defeasible inheritance have been largely investigated. In this paper, we consider two such extensions, namely (i) the extension of DLs with a typicality operator T, having the properties of Preferential nonmonotonic entailment P, and (ii) its variant with a typicality operator having the properties of the stronger Rational entailment R. The first one has been proposed in [6]. Here, we investigate the second one and we show, by a representation theorem, that it is equivalent to the approach to preferential subsumption proposed in [3]. We compare the two extensions, preferential and rational, and argue that the first one is more suitable than the second one to reason about typicality, as the latter leads to very unintuitive inferences.

We extend the Description Logic ALC with a "typicality" operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + T. The typicality operator is intended to select the "most normal" or "most typical" instances of a concept. In our framework, knowledge bases may then contain, in addition to ordinary ABoxes and TBoxes, subsumption relations of the form "T(C) is subsumed by P", expressing that typical C-members have the property P. The semantics of a typicality operator is defined by a set of postulates that are strongly related to Kraus-Lehmann-Magidor axioms of preferential logic P. We first show that T enjoys a simple semantics provided by ordinary structures equipped with a preference relation. This allows us to obtain a modal interpretation of the typicality operator. We show that the satisfiability of anALC+Tknowledge base is decidable and it is precisely EXPTIME. We then present a tableau calculus for deciding satisfiability of ALC + T knowledge bases. Our calculus gives a (suboptimal) nondeterministic-exponential time decision procedure for ALC + T. We finally discuss how to extend ALC + T in order to infer defeasible properties of (explicit or implicit) individuals. We propose two alternatives: (i) a nonmonotonic completion of a knowledge base; (ii) a "minimal model" semantics for ALC + T whose intuition is that minimal models are those that maximise typical instances of concepts.

We present tableau calculi for the logics of nonmonotonic reasoning defined by Kraus, Lehmann and Magidor (KLM). We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative, and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered and we study their complexity.

We present a tableau calculus for some fundamental systems of propositional conditional logics. We consider the conditional logics that can be characterized by preferential semantics (i.e., possible world structures equipped with a family of preference relations). For these logics, we provide a uniform completeness proof of the axiomatization with respect to the semantics, and a uniform labeled tableau procedure.