A calculus for four-valued sequential logic

A calculus for four-valued sequential logic

We present a complete axiomatisation for four-valued sequential logic. It consists of nine axioms, from which all valid laws can be derived by equational reasoning. These nine axioms are independent of each other. © 2011 Elsevier B.V. All rights reserved.

A Calculus for Sequential Logic with Values

A Sequent Calculus for Reasoning in Four-Valued Description Logics

Description Logics (DLs, for short) provide a logical reconstruction of the so-called frame-based knowledge representation languages. Originally, four-valued DLs have been proposed in order to develop expressively powerful DLs with tractable subsumption algorithms. Recently, four-valued DLs have been proposed as a model for (multimedia) document retrieval. In this context, the main reasoning ta...

Four-Valued Semantics for Default Logic

Reiter’s default logic suffers the triviality, that is, a single contradiction in the premise of a default theory leads to the only trivial extension which everything follows from. In this paper, we propose a default logic based on fourvalued semantics, which endows default logic with the ability of handling inconsistency without leading to triviality. We define four-valued models for default t...

Bitopology and Four-valued Logic

Bilattices and d-frames are two different kinds of structures with a four-valued interpretation. Whereas d-frames were introduced with their topological semantics in mind, the theory of bilattices has a closer connection with logic. We consider a common generalisation of both structures and show that this not only still has a clear bitopological semantics, but that it also preserves most of the...