Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

The role of logic in knowledge representation and commonsense reasoning

Abstract: This paper examines the role that formal logic ought to play in representing and reasoning with commonsense knowledge. We take issue with the commonly held view (as expressed by Newell [1980]) that the use of representations based on formal logic is inappropriate in most applications of artificial intelligence. We argue to the contrary that there is an important set of issues, involving incomplete knowledge of a problem situation, that so far have been addressed only by systems based on formal logic and deductive inference, and that, in some sense, probably can be dealt with only by systems based on logic and deduction. We further argue that the experiments of the late 1960s on problem-solving by theorem-proving did not show that the use of logic and deduction in AI systems was necessarily inefficient, but rather that what was needed was better control of the deduction process, combined with more attention to the computational properties of axioms.

Multiple-conclusion logic

Abstract: Multiple-conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions.

Reasoning with logical bilattices

Abstract: The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. The outcome are paraconsistent logics with a lot of desirable properties. A preliminary version of this paper appears in Arieli and Avron (1994).