Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets

Multimedia reasoning, which is suitable for, among others, multimedia content analysis and high-level video scene interpretation, relies on the formal and comprehensive conceptualization of the represented knowledge domain. However, most multimedia ontologies are not exhaustive in terms of role definitions, and do not incorporate complex role inclusions and role interdependencies. In fact, most multimedia ontologies do not have a role box at all, and implement only a basic subset of the available logical constructors. Consequently, their application in multimedia reasoning is limited. To address the above issues, VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a DL-safe ruleset has been introduced for next-generation multimedia reasoning. In contrast to the common practice, the formal grounding has been set in one of the most expressive description logics, and the ontology validated with industry-leading reasoners, namely HermiT and FaCT++. This paper also presents best practices for developing multimedia ontologies, based on my ontology engineering approach

Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems

The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Castro, Pablo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Aguirre, Nazareno M.. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Maibaum, Thomas S.E.. Mc Master University; Canad

Formally Verified Tableau-Based Reasoners for a Description Logic

Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. One of the most basic description logics is ALC , used as a basis from which to obtain others. Description logics are particularly important to provide a logical basis for the web ontology languages (such as OWL) used in the Semantic Web. In order to increase the reliability of the Semantic Web, formal methods can be applied, and in particular formal verification of its reasoning services can be carried out. In this paper, we present the formal verification of a tableau-based satisfiability algorithm for the logic ALC . The verification has been completed in several stages. First, we develop an abstract formalization of satisfiability-checking of ALC -concepts. Secondly, we define and formally verify a tableau-based algorithm in which the order of rule application and branch selection can be flexibly specified, using a methodology of refinements to transfer the main properties from the ALC abstract formalization. Finally, we obtain verified and executable reasoners from the algorithm via a process of instantiation.Ministerio de Ciencia e Innovación TIN2009-09492Junta de Andalucía TIC-0606