This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. ...

In this paper, a linguistic truth-value lattice proposition logic system LTV LP (X) is presented firstly. It is an useful and reasonable tool to deal with the linguistic term set including linear ordered set and non-linear ordered set. Then an operator linguistic truth-value lattice-valued proposition logic OLTV LP (X) is given. The OLTV LP (X) can provide a theoretical model for multi-evaluato...

Abstract This paper is dedicated to extending and adapting modal logic the approach of fractional semantics classical logic. a multi-valued governed by pure proof-theoretic considerations, whose truth-values are rational numbers in closed interval $[0,1]$ . Focusing on K , proposed methodology relies three key components: bilateral sequent calculus, invertibility logical rules, stability (proof...

In [10] Osorio et al. introduced a paraconsistent three-valued logic, the logic CG3 which was named after the logic G ′ 3 due to the close relation between them. Authors defined CG3 via the three-valued matrix that defines G3 but changing the set of designated truth values. In this article we present a brief study of the Kripke-type semantics for some logics related with CG3 before constructing...

In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a recent work by Lifschitz, Pearce and Valverde, strong equivalence can be simply reduced to equivalence in the logic of Here-and-There (HT). In this paper we pro...

Fundamental discrepancy between first order logic and statistical inference (global versus local properties of universe) is shown to be the obstacle for integration of logic and probability in L.p. logic of Bacchus. To overcome the counterintuitiveness of L.p. behaviour, a 3-valued logic is proposed.

Modular programs are built as a combination of separate modules, which may be developed and veriied separately. Therefore, in order to reason over such programs, compositionality plays a crucial role: the semantics of the whole program must be obtainable as a simple function from the semantics of its individual modules. In the eld of logic programming, the need for a compositional semantics has...

This paper outlines the Chinese research on mathematical logic and foundations of mathematics. Firstly, it presents introduction spread in China, especially teaching translation initiated by Bertrand Russell’s lectures country. Secondly, after founding People’s Republic China. The this period experienced a short revival under criticism Soviet Union, explorations heavy influence Cultural Revolut...

Multi-valued logics can be effectively used to reason about incomplete and/or inconsistent systems, e.g. during early software requirements or as the systems evolve. In our earlier work we identified a useful family of multi-valued logics: those specified over finite distributive lattices where negation preserves involution, i.e., , , -/.0for every element of the logic. Model-checking over this...