Modal and temporal logics are finding new and varied applications in Computer Science in fields as diverse as Artificial Intelligence [Marek et al.,1991], Models for Concurrency [Stirling, 1992] and Hardware Verification [Nakamura et al.,1987]. Often the eventual use of these logics boils down to the task of deducing whether a certain formula of a logic is a logical consequence of a set of other formula of the same logic. The method of semantic tableaux is now well established in the field of Automated Deduction [Oppacher and Suen, 1988; Baumgartner et al., 1995; Beckert and Possega, 1995] as a viable alternative to the more traditional methods based on resolution [Chang and Lee, 1973]. In this chapter we give a systematic and unified introduction to tableau methods for automating deduction in modal and temporal logics. We concentrate on the propositional fragments restricted to a two-valued (classical) basis and assume some prior knowledge of modal and temporal logic, but give a brief overview of the associated Kripke semantics to keep the chapter self-contained.

Tableau Methods for Modal and Temporal Logics

Knowledge representation and reasoning is the foundation of artificial intelligence, declarative programming, and the design of knowledge-intensive software systems capable of performing intelligent tasks. Using logical and probabilistic formalisms based on answer set programming (ASP) and action languages, this book shows how knowledge-intensive systems can be given knowledge about the world and how it can be used to solve non-trivial computational problems. The authors maintain a balance between mathematical analysis and practical design of intelligent agents. All the concepts, such as answering queries, planning, diagnostics, and probabilistic reasoning, are illustrated by programs of ASP. The text can be used for AI-related undergraduate and graduate classes and by researchers who would like to learn more about ASP and knowledge representation.

Knowledge Representation, Reasoning, and the Design of Intelligent Agents: The Answer-Set Programming Approach

1This book was published 1986 by the Akademie-Verlag Berlin, Volume 32 in the series “Mathematical Research”; Lector was Dr. Reinhard Hoppner. It was printed in the German Democratic Republic. It has been transferred into LATEX by Ulrich Thiemann. In connection with this translation also the notation for the direction used for the composition of homomorphisms has been changed (the first morphism is written to the right of the second one, etc.). So far most of the diagrams are still missing. Also an index is still missing. The errors and misprints in the original version have not yet been corrected. The bibliography has been extended about 1990 and not yet been updated – moreover, it may still contain many titles, which treat “partial operations” (which was the keyword for the search in the Zentralblatt), but which are not really concerned with partial algebras in the sense of this book. In order to get a better idea of the material in the book, the article: Tools for a Theory of Partial Algebras, which has been published in: General Algebra and Applications (Eds.: K.Denecke and H.-J.Vogel), Research and Exposition in Mathematics, Vol. 20, Heldermann Verlag Berlin, 1993, pp. 12–32, has been added to a revised introduction.

A Model Theoretic Oriented Approach to Partial Algebras

Equilibrium logic is a general purpose nonmonotonic reasoning formalism closely aligned with answer set programming (ASP). In particular it provides a logical foundation for ASP as well as an extension of the basic syntax of answer set programs. We present an overview of equilibrium logic and its main properties and uses.

Equilibrium logic

Publisher Summary
An algebraic specification is a description of one or more abstract data types. There are three main semantic approaches to algebraic specifications: (1) the initial algebra approach, (2) the terminal algebra approach, and (3) the loose approach. A fourth approach that is mainly of theoretical interest uses iso-initial algebras. This chapter reviews the basic concepts for the theory of algebraic specifications. It also describes the notion of an abstract data type and discusses its basic properties. The chapter also describes four other semantic concepts and algebras for specifying nondeterminism and concurrency. The chapter discusses the existence of initial and terminal algebras, the lattice structure of the models, and the expressive power of initial and terminal algebra specifications. The chapter also presents two additional concepts for algebraic specifications, which are both practically and theoretically essential: (1) hidden symbols and (2) constructors. The chapter also presents a general approach to structured specifications.

CHAPTER 13 – Algebraic Specification

Duplication-free tableau calculi and related cut-free sequent calculi for the interpolable propositional intermediate logics

On etudie les relations entre verite constructive et verite classique d'un point de vue unifie

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A constructivism based on classical truth

Some techniques for the study of intermediate constructive logics are illustrated. In particular a general characterization is given of maximal constructive logics from which a new proof of the maximality of MV (Med- vedev's logic of finite problems ) can be obtained. Some semantical notions are also introduced, allowing a new characterization of MV, from which a new proof of a conjecture of Friedman's and a new family of principles valid in MV can be extracted.

/pdf/some-results-on-intermediate-constructive-logics-49fitrzb9w.pdf

Pierangelo Miglioli

Papers

Duplication-free tableau calculi and related cut-free sequent calculi for the interpolable propositional intermediate logics

A constructivism based on classical truth

Some results on intermediate constructive logics.

On the power of model theory in specifying abstract data types and in capturing their recursiveness

Abstract parametric classes and abstract data types defined by classical and constructive logical methods