Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modeling the dynamics of a game frame whose states may correspond to different game forms. The two classes of effectivity functions studied are the families of playable and truly playable effectivity fun...

Conflict-directed clause learning (CDCL) is the basis of SAT solvers with impressive performance on many problems. CDCL with restarts (CDCL-R) has been shown to have essentially the same reasoning power as unrestricted resolution (formally, they p-Simulate each other). We show that this property generalizes to multi-valued CNF formulas. In particular, for Signed (or Multi-Valued) CNF formulas, ...

In this paper several systems of modal logic based on four-valued matrices are presented. We start with pure modal logics, i.e. modal logics with modal operators as the only operators, using the Polish framework of structural consequence relation. We show that with a four-valued matrix we can define modal operators which have the same behavior as in pure S5 (S5 with only modal operators). We th...

In this paper we illustrate by means of an example, namely SHn-logics, a method for translation to clause form and automated theorem proving for first-order many-valued logics based on distributive lattices with operators.

Preamble This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robi...

Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic...

The prenex fragments of first-order infinite-valued Gödel logics are classified. It is shown that the prenex Gödel logics characterized by finite and by uncountable subsets of [0,1] are axiomatizable, and that the prenex fragments of all countably infinite Gödel logics are not axiomatizable.

In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language is based on an underlying Heyting algebra which provides the space of truth values. The lattice of truth values is explicitly represented in the language by a set of special constants and this allows for forming weak, generalized, many-valued analogs of all classical modal axioms. Weak axioms of th...

The higher-order types of Herbrand interpretations for databases arise often in practice when we have to deal with uncertain or imprecise information, or in constrained databases. They are a consequence of the introduction of a kind of the observational equivalence for the hidden information in the ordinary Herbrand interpretations. It means that the logics for such databases are particular fun...