Signed formula can be used to reason about a wide variety of multiple-valued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in 26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint logic programming. Applications to bilattice logic programming and truth-maintenance are considered.

One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.

Classical Logic is bivalent in that it admits exactly two truth-values: the true and the false. Many-valued logics, in contrast, allow for the consideration of arbitrarily large classes of truth-values. To export the canonical notion of entailment to the realm of many-valuedness, the trick is to characterize any such class of truth-values by saying that some of these values are ‘designated’. On...

In this paper we will prove the equivalence between L-valued logics and L-indexed families of bivaluated logics. It is also proved that this equivalence can be used as a tool for checking compactness and decidability properties of a L-valued logic.

A drawback of many logics for reasoning on Semantic Web ontologies is the Principle of Explosion in case of inconsistent data. Considering a four-valued semantics, inconsistencies can be tolerated such that paraconsistency is obtained. We extend Belnap’s four-valued logic to a four-valued first-order logic with implication and equality, and we develop a method for translating formulas to a repr...

Multi-valued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. This paper presents a symbolic model checker for multi-valued temporal logics. The model checker works for any multivalued ...

We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the Kripke possible-world semantics for it. Such a new framework offers a new semantics for many-valued logics based on the truth-invariance entailment. Consequently...

Through minimal-model semantics, three-valued logics provide an interesting formalism for capturing reasoning from inconsistent information. However, the resulting paraconsistent logics lack so far a uniform implementation platform. Here, we address this and specifically provide a translation of two such paraconsistent logics into the language of quantified Boolean formulas (QBFs). These formul...

In this paper a comparative study of many-valued logics, fuzzy logics and the theory of graded consequence has been made focussing on consequence, inconsistency and sorites paradox.