Showing papers on "Paraconsistent logic published in 1982"

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.

To be and not to be: Dialectical tense logic

Abstract: The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to ℸp being true where a contradiction is realized. The second part of the paper specifies a formal logic which accommodates this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: “Whatever holds up to the limit holds at the limit”. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed.

Logic, Quantum Logic and Empiricism

Abstract: This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong (1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation crucially does not. The argument is conducted via a thorough analysis of how the meet, join and complementation operations are defined in the relevant logical structures, respectively Boolean- and ortholattices (3). Since Putnam wishes to reinstate a realist interpretation of quantum mechanics, we ask how quantum logic can be a logic of realism. We show that it certainly cannot be a logic of bivalence realism (i.e., of truth and falsity), although it is consistent with some form of ontological realism (4). Finally, we show...

Deduction theorems for weak implicational logics

Abstract: The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics.