Belnap's logic and conditional composition

A generalization of ACP using Belnap's logic

ACP is combined with Belnap’s four-valued logic via conditional composition (if–then–else). We show that the operators of ACP can be seen as instances of more general, conditional operators. For example, both the choice operator + and δ (deadlock) can be seen as instances of conditional composition, and the axiom x + δ = x follows from this perspective. Parallel composition is generalized to th...

Combining Explicit Negation and Negation by Failure via Belnap's Logic Combining Explicit Negation and Negation by Failure via Belnap's Logic

This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation, allowing two diierent forms of uncertainty reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued log...

A Critical Examination of Ibn-Sina’s Theory of the Conditional Syllogism

This paper will examine Ibn Sina’s theory of the Conditional Syllogism from a purely logical point of view, and will lay bare the principles he adopted for founding his theory, and the reason why the newly introduced part of his logic remained undeveloped and eventually was removed from the texts of logic in the later Islamic tradition. As a preliminary discussion, this paper briefly examines I...

Combining Explicit Negation and Negation by Failure Via Belnap's Logic

This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two diierent forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and a...

A knowledge representation based on the Belnap's four-valued logic