We introduce a family of partial stable model semantics for logic programs with arbitrary aggregate relations. The semantics are parametrized by the interpretation of aggregate relations in three-valued logic. Any semantics in this family satisfies two important properties: (i) it extends the partial stable semantics for normal logic programs and (ii) total stable models are always minimal. We ...

The coincidence of the declarative and procedural interpretations of logic programs does not apply to Prolog programs, due to the depth-rst left-to-right evaluation strategy of Prolog interpreters. We propose a semantics for Prolog programs based on a four-valued logic. The semantics is based on a new concept of completion analogous to Clark's and it enjoys the nice properties of the declarativ...

The Loś-Tarski Theorem and the ChangLoś-Susko Theorem, two classical results in Model Theory, are extended to the infinitevalued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic forcing for Lukasiewicz logic [1]. Key-words: First Order Many-Valued Logic, Lukasiewicz logic, Model Theory.

Uncertainty reasoning is one of the important issues of many research fields, such as artificial intelligence, knowledge-based systems, data-mining etc.. This paper proposes the theory of uncertainty reasoning in the “If...then...” type uncertainty reasoning mode based on the lattice-valued first-order logic Lvfl. The “If...then...” rule presented here is the rule in which both antecedent and c...

Most verification approaches assume a mathematical formalism in which functions are total, even though partial functions occur naturally in many applications. Furthermore, although there have been various proposals for logics of partial functions, there is no consensus on which is “the right” logic to use for verification applications. In this paper, we propose using a three-valued Kleene logic...

Smarandache (2003) introduced a new set-valued fuzzy logic called (nonstandard) neutrosophic by using Robinson’s nonstandard analysis. However, its definition involved many errors including the illegal use of In this paper, we provide rigorous logic. All in original are addressed. We then point out some paradoxes Finally formulate with no

We give a classification of dual functions, they are m -al functions. We call a function m-al with respect to an operator if the operator lives any function unchanged after m times of using the operator. And 2 ≤ m ≤ k. Functions with different m have very different properties. We give theoretical results for clones of self-dual (m = 2) and selfk -al (m = k) functions in k -valued logic at k ≤ 3...

Computing certain answers is the preferred way of answering queries in scenarios involving incomplete data. This, however, is computationally expensive, so practical systems use efficient techniques based on a particular three-valued logic, although this often leads to

We develop a general study of graded consequence (of many-valued logic) in an institution theoretic (in the sense of Goguen and Burstall) style. This means both syntax and semantics are considered fully abstract, as well as the satisfaction between them. Our approach contrasts to other approaches on many-valued logic in that it is a multisignature one, in the spirit of institution theory. We co...

Even though it is not very often admitted, partial functions do play a signiicant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional lo...