Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Uma linguagem para formalização de discursos com base em ontologias

Tese (doutorado)—Universidade de Brasília, Faculdade de Ciência da Informação, Programa de Pós-Graduação em Ciência da Informação, 2015.Esta pesquisa propõe a arquitetura da informação de uma linguagem formal textual para representar discursos sobre entidades ontológicas e obter deduções a respeito de ontologias de domínio. Por meio do paradigma de metamodelagem, a linguagem permite tratamento de ontologias heterogêneas que podem ser descritas como instâncias de uma ou mais ontologias de fundamentação. A linguagem suporta comportamentos clássicos e modais sustentados por noções de prova baseadas no paradigma de Programação em Lógica (Modal). O arcabouço modal desenvolvido possibilita que diferentes interpretações modais sejam introduzidas às especificações das ontologias, e contempla especialmente sistemas baseados em lógicas de múltiplos agentes. Uma sistematização do fragmento endurante da Unified Foundational Ontology (UFO) é realizada com objetivo de compor parte do marco teórico que fundamenta a proposta e de servir de exemplo de instanciação do arcabouço desenvolvido. Como resultados complementares, destacam-se: uma sistematização de um conjunto ampliado de regras para produção de modelos conceituais e um glossário detalhado de termos e conceitos da UFO-A; protótipos funcionais que implementam os sistemas elaborados; traduções das teorias descritas no arcabouço proposto para linguagens visuais, como extensões da representação gráfica da OntoUML; e discussões a respeito da integração de Arquitetura da Informação, Modelagem Conceitual e Programação em Lógica (Modal) no contexto social aplicado.This research proposes the information architecture of a textual formal language to represent and reason about ontological entities based on foundational ontologies. Through metamodeling, the language is able to deal with heterogeneous ontologies that can be described as instances of one or more foundational ontology. The language provides classic and modal inference mechanisms supported by proof notions based on the (Modal) Logic Programming paradigm. The modalities introduced by the modal framework allow a wide range of interpretations, including multi-agent systems. A systematization of the endurant fragment of the Unified Foundational Ontology (UFO) is produced in order to compose part of the theoretical framework underlying the proposal, and to serve as an example instantiating the developed framework. As complementary results we highlight: a systematization of an extended set of rules for conceptual modeling and a detailed glossary of terms and concepts of UFO-A; functional prototypes implementing the developed systems; translations of the theories described as instances of the framework to diagramatic representations, as extensions of the OntoUML visual language; and discussions regarding the integration of Information Architecture, Conceptual Modeling and Logic Programming within Applied Social Science

IOS Press The Modal Query Language MDatalog

Abstract. We propose a modal query language called MDatalog. A rule of an MDatalog program is a universally quantified modal Horn clause. This language is interpreted in fixed-domain first-order modal logics over signatures without functions. We give algorithms to construct the least models for MDatalog programs. We show PTIME complexity of computing queries for a given MDatalo

The data complexity of MDatalog in basic modal logics

Abstract. We study the data complexity of the modal query language MDatalog and its extension eMDatalog in basic modal logics. MDatalog is a modal extension of Datalog, while eMDatalog is the general modal Horn fragment with the allowedness condition. As the main results, we prove that the data complexity of MDatalog and eMDatalog in K4, KD4, and S4 is PSPACE-complete, in K is coNP-complete, and in KD, T, KB, KDB,andB is PTIME-complete.

On modal deductive databases

We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-set transformation are proved for the multimodal logics of belief KDI4s5, KDI45, KD4s5s, KD45(m), KD4Ig5a, and the class of serial contextfree grammar logics. We also show that MDatalog has PTIME data complexity in the logics KDI4s5, KDI45, KD4s5s, and KD45(m).

A Computational Method for Modal Deductive Databases

We present a query language called MDatalog, which is an extension of Datalog for multimodal deductive database. We de ne modal relational algebras and give the seminaive evaluation algorithm and the magic-set transformation for multimodal deductive databases. Our formulation is general, however, the results are proved only for the multimodal logics KDI4s 5, KDI45, KD4s5s , KD45 (m) , which are multimodal extensions of the monomodal logic KD45. The logics KDI4s5 and KDI45 are intended for reasoning about multi-degree belief, while KD4s5s is for use in distributed systems of belief, and KD45 (m) is for reasoning about epistemic states of agents. We show that MDatalog has PTIME data complexity in these logics