Towards possibilistic fuzzy answer set programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers

Reducing fuzzy answer set programming to model finding in fuzzy logics

In recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalisms allow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners

On the Application of Argument Accrual to Reasoning with Inconsistent Possibilistic Ontologies

We present an approach for performing instance checking in a suitable subset of possibilistic description logic programming ontologies by using argument accrual. Ontologies are interpreted in possibilistic logic programming under Dung's grounded semantics. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

On the Application of Argument Accrual to Reasoning with Inconsistent Possibilistic Ontologies

We present an approach for performing instance checking in a suitable subset of possibilistic description logic programming ontologies by using argument accrual. Ontologies are interpreted in possibilistic logic programming under Dung's grounded semantics. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allows to reason with modus ponens and constructive dilemmas. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.Facultad de Informátic

Towards Contingent World Descriptions in Description Logics

The philosophical, logical, and terminological junctions between Description Logics (DLs) and Modal Logic (ML) are important because they can support the formal analysis of modal notions of ‘possibility’ and ‘necessity’ through the lens of DLs. This paper introduces functional contingents in order to (i) structurally and terminologically analyse ‘functional possibility’ and ‘functional necessity’ in DL world descriptions and (ii) logically and terminologically annotate DL world descriptions based on functional contingents. The most significant contributions of this research are the logical characterisation and terminological analysis of functional contingents in DL world descriptions. The ultimate goal is to investigate how modal operators can – logically and terminologically – be expressed within DL world descriptions