In this paper we continue the theoretical study of the possible applications of the ∆-tree data structure for multiple-valued logics, specifically, to be applied to signed propositional formulas. The ∆-trees allow a compact representation for signed formulas as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfi...

We present n-valued rst-order logics with a purely proba-bilistic semantics. We then introduce a new probabilistic semantics of n-valued rst-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics Ln. Within this semantics, closed formulas of classical rst-order logics that are logically equivalent in the classical ...

This paper describes our multi-valued symbolic modelchecker χChek. χChek is a generalization of an existing symbolic model-checking algorithm for a multi-valued extension of the temporal logic CTL. Multi-valued modelchecking supports reasoning with values other than just TRUE and FALSE. Multi-valued logics are useful in software engineering because they support explicit modeling of uncertainty,...

This paper describes our multi-valued symbolic modelchecker χChek. χChek is a generalization of an existing symbolic model-checking algorithm for a multi-valued extension of the temporal logic CTL. Multi-valued modelchecking supports reasoning with values other than just TRUE and FALSE. Multi-valued logics are useful in software engineering because they support explicit modeling of uncertainty,...

We present a general framework that allows to construct systematically analytic calculi for a large family of (propositional) many-valued logics — called projective logics — characterized by a special format of their semantics. All finite-valued logics as well as infinite-valued Gödel logic are projective. As a case-study, sequent of relations calculi for Gödel logics are derived. A comparison ...

Classical logic cannot be used to effectively reason about systems with uncertainty (lack of essential information) or inconsistency (contradictory information often occurring when information is gathered from multiple sources). In this paper we propose the use of quasi-boolean multi-valued logics for reasoning about such systems. We also give semantics to a multi-valued extension of CTL, descr...

Introduction. Classical logics are based on the bivalence principle, that is, the set of truth-values V has cardinality |V | = 2, usually with V = {T,F} where T and F stand for truthhood and falsity, respectively. Many-valued logics generalize this requirement to more or less arbitrary sets of truth-values, rather referred to as truth-degrees in that context. Popular examples of many-valued log...

s of the Talks In the order in which the talks were given. Walter Carnielli – Non-deterministic Semantics 5 Matthias Baaz – Analytic Calculi for Many-valued Logics 5 Hiroakira Ono – Many-valued Logics as Logics without the Contraction Rule 6 Reiner Hähnle – Proof Theory of Many-valued Logic and Hardware Design 7 Gonzalo Escalada-Imaz – Determining the Truth Degree in Real Time Settings 7 Peter ...