In 4] , the semantics of monotonic (i.e. not-free) extended logic programs (ELPs) has been rephrased in three-valued logic for two purposes: achieving tractable reasoning with incomplete information and understanding the relationships between the existing semantics and many-valued logics. In this paper, we generalize this approach to unrestricted ELPs. We obtain a unifying view of many formalis...

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...

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and compl...

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...

We introduce a new approach to conditional probability over many-valued events, which is based on bets. Then we show that this approach fits with Kroupa’s approach, and we give two characterizations of coherence for books on conditional many-valued events, the first one based on states, and the second one based on logical coherence of a suitable theory on many-valued logic.

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development ar...

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...