Complexity of Non-Monotonic Logics

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been considered, e.g., extension with default rules, extension with modal belief operators, or modification of the semantics. In this survey we consider a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription. Additionally, we consider abduction, where one is not interested in inferences from a given knowledge base but in computing possible explanations for an observation with respect to a given knowledge base. Complexity results for different reasoning tasks for propositional variants of these logics have been studied already in the nineties. In recent years, however, a renewed interest in complexity issues can be observed. One current focal approach is to consider parameterized problems and identify reasonable parameters that allow for FPT algorithms. In another approach, the emphasis lies on identifying fragments, i.e., restriction of the logical language, that allow more efficient algorithms for the most important reasoning tasks. In this survey we focus on this second aspect. We describe complexity results for fragments of logical languages obtained by either restricting the allowed set of operators (e.g., forbidding negations one might consider only monotone formulae) or by considering only formulae in conjunctive normal form but with generalized clause types. The algorithmic problems we consider are suitable variants of satisfiability and implication in each of the logics, but also counting problems, where one is not only interested in the existence of certain objects (e.g., models of a formula) but asks for their number.Comment: To appear in Bulletin of the EATC

Uma proposta de interdisciplinaridade entre arquitetura da informação e ciência da computação : linguagem “SOWL” para as ontologias da Web utilizando o formalismo dos grafos conceituais

Tese (doutorado)—Universidade de Brasília, Faculdade de Ciência da Informação, 2013.A Web Semântica, sendo a nova visão proposta pelo World Wide Web Consortium (W3C) para a estrutura atual da Web, é destinada a aumentar as possibilidades que ela oferece e, dessa forma, tornar seus recursos mais acessíveis para as máquinas. Entretanto, as técnicas de raciocínio de inferência utilizadas atualmente sobre os conhecimentos descritos pelas linguagens de representação de semânticas Web se baseiam somente sobre as capacidades inferenciais do formalismo de lógicas de descrição e os da lógica de predicados, já largamente utilizados nos motores de inferências. Este fato introduz a importância das pesquisas que tratam da representação do conhecimento e das técnicas de raciocínio sobre as ontologias na ótica da Web Semântica. O presente trabalho se propõe a estudar a capacidade dos grafos conceituais para representar e operacionalizar as ontologias da Web, assim como as contribuições dessa abordagem, de um ponto de vista simbólico (poder e facilidade de representação e interpretação) e inferencial (tipos de inferência aplicáveis a esse formalismo). Sendo a Arquitetura da Informação uma disciplina indissociavelmente ligada às tecnologias da informação, o presente trabalho é uma proposta para a interdisciplinaridade entre esta e a Ciência da Computação. _______________________________________________________________________________________ ABSTRACTThe Semantic Web, being the new vision proposed by World Wide Web Consortium (W3C), to the current structure of the Web, is designed to increase the possibilities that it provides, and thereby, render its resources more accessible to machines. However, the techniques of inference on the knowledge described by representation languages of Semantic Web are based only on the inferential on formalism of description logics capabilities and formalisms of predicate logic, already widely used in the inferences engines. This fact introduces the importance of research that deals with the knowledge representation and reasoning techniques on ontologies from the perspective of the Semantic Web. The present work was geared towards the capacity of conceptual graphs to represent and operationalize the Web ontologies, as well as the contributions of this approach, as a symbolic viewpoint (power and representation, and interpretation facility) and inferential (inference types applicable to this formalism). Since the Information Architecture is one discipline inextricably linked to information tecnology, the present work is a proposal for the interdisciplinarity between this and Computer Science