Some multi-agent scenarios call for the possibility of evaluating specifications in a richer domain of truth values. Examples include runtime monitoring of a temporal property over a growing prefix of an infinite path, inconsistency analysis in distributed databases, and verification methods that use incomplete anytime algorithms, such as bounded model checking. In this paper, we present multi-valued alternating-time temporal logic ( mv-ATL → ∗ ), an expressive logic to specify strategic abilities in multi-agent systems. It is well known that, for branchingtime logics, a general method for model-independent translation from multi-valued to two-valued model checking exists. We show that the method cannot be directly extended to mv-ATL → ∗ . We also propose two ways of overcoming the problem. Firstly, we identify constraints on formulas for which the model-independent translation can be suitably adapted. Secondly, we present a model-dependent reduction that can be applied to all formulas of mv-ATL → ∗ . We show that, in all cases, the complexity of verification increases only linearly when new truth values are added to the evaluation domain. We also consider several examples that show possible applications of mv-ATL → ∗ and motivate its use for model checking multi-agent systems.

In the paper Cut-free ordinary sequent calculi for logics having generalized finite-valued semantics by A. Avron, J. Ben-Naim, and B. Konikowska. (Logica Universalis, 1:41–69, 2006), a general method was developed for generating cut-free ordinary sequent calculi for logics that can be characterized by finite-valued semantics based on non-deterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made by applying that method to a certain crucial family of thousands of paraconsistent logics, all belonging to the class of C-systems. For that family, the method produces in a modular way uniform Gentzen-type rules corresponding to a variety of axioms considered in the literature.

This paper makes a substantial step towards automatization of Para consistent reasoning by providing a general method for a systematic and modular generation of cut-free calculi for thousands of Para consistent logics known as Logics of Formal (In)consistency. The method relies on the use of non-deterministic semantics for these logics.

We examine the issue of collecting and processing information from various sources, which involves handling incomplete and inconsistent information. Inspired by the framework first proposed by Belnap, we consider structures consisting of information

The paper introduces a notion of an algebra corresponding to the three-valued logical calculus designed by McCarthy for computation purposes and used in several existing software system. The algebra, called McCarthy algebra, is a generalization of a Boolean algebra. It is defined extensionally, but a set of sound equality axioms is also given. From these axioms, various non-classical properties of the elements of such algebras are deduced. A representation theorem for two classes of McCarthy algebras is presented.