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This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences. [ABSTRACT FROM AUTHOR]

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: All x are y and Some x are y , There are at least as many x as y , and There are more x than y. Here x and y range over subsets (not elements) of a given infinite set. Moreover, x and y may appear complemented (i.e., as x and ӯ), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. There are efficient algorithms for proof search and model construction. [ABSTRACT FROM AUTHOR]

We add Most X are Y to the syllogistic logic of All X are Y and Some X are Y. We prove soundness, completeness, and decidability in polynomial time. Our logic has infinitely many rules, and we prove that this is unavoidable. [ABSTRACT FROM AUTHOR]

The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio ad absurdum is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments. [ABSTRACT FROM AUTHOR]

Discusses the concept of quantum logic in relation to quantum computing. Variation in the definition of quantum logic; Consideration of the lattice of closed subspaces of a Hilbert space; Theoretical basis of quantum computing; Observation that quantum logic is not a finite-valued logic; Illustration of some open problems.