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Space Complexity in Propositional Calculus
SIAM Journal on Computing, 2000Summary: We study space complexity in the framework of propositional proofs. We consider a natural model analogous to Turing machines with a read-only input tape and such popular propositional proof systems as resolution, polynomial calculus, and Frege systems.
Eli Ben-Sasson +3 more
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Completeness of the propositional calculus
Journal of Symbolic Logic, 1938The completeness of the prepositional calculus was first proved by Post. His somewhat condensed proof has been succeeded by more detailed presentations of substantially the same argument, and also by several proofs of radically different forms. The present paper contains still another proof, offered because of its relative simplicity.
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Fragments of the propositional calculus
Journal of Symbolic Logic, 1949Of the several methods for proving the completeness of sets of axioms for the prepositional calculus perhaps the simplest is due to Kalmár, although it does not appear to be widely known. In this paper we generalize Kalmár's method to indicate how to obtain a complete axiomatization of any fragment of the propositional calculus which includes material ...
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1983
Publisher Summary This chapter discusses propositional calculus. Although the special case of propositional variables really suffices for studying propositional formulas, it is useful in order to include later applications, to allow the more general case of an arbitrary language of atoms.
Elaine J. Weyuker, Martin Davis
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Publisher Summary This chapter discusses propositional calculus. Although the special case of propositional variables really suffices for studying propositional formulas, it is useful in order to include later applications, to allow the more general case of an arbitrary language of atoms.
Elaine J. Weyuker, Martin Davis
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1987
Sentences may be combined in various ways to form more complicated sentences. Let us consider only truth-functional combinations, in which the truth or falsity of the new sentence is determined by the truth or falsity of its component sentences.
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Sentences may be combined in various ways to form more complicated sentences. Let us consider only truth-functional combinations, in which the truth or falsity of the new sentence is determined by the truth or falsity of its component sentences.
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Intuitionistic Propositional Calculus [PDF]
, 1995 It seems that, over many centuries, no philosopher or mathematician ever seriously questioned Aristotle’s law of the excluded third: for every proposition p, either p or not p, symbolically p V ¬p. In retrospect, it appears that Aristotle himself had some doubts about applying this law when talking about events in time, e.g., when p was the proposition:
Joachim Lambek, W. S. Anglin
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Intuitionistic Propositional Calculus
1992Intuitionism is deemed to be the most important non-classical logic calculus. There is not much exaggeration in saying that it has arisen accidentally, as an attempt to axiomatize a certain three-valued logic. In fact, it should be rather regarded as the result of a programme of putting constraints on the laws and rules of classical logic.
Leonard Bolc, Piotr Borowik
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Properties of the Propositional Calculus
1975The properties of the Propositional Calculus that are of interest are those that arise in studying the relation between truth and proof. These properties are important features in the study of any formal system of reasoning, and we begin with some general definitions.
Donald W. Barnes, John Mack
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The PRIZ system and propositional calculus
Cybernetics, 1983Summary: In this paper we show that the design of the PRIZ system [\textit{M. I. Kakhro, A. P. Kal'ya}, and \textit{E. Kh. Tyugu}: The PRIZ instrumental system of computer programming (Russian) (Moskva, 1981)] contains a program of search for a deduction in intuitionistic (Heyting, or constructive) propositional calculus [\textit{S. C.
É. Kh. Tyugu +3 more
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Applications of Propositional Calculus
1993We look at two applications of propositional calculus. The first is its use in solving various “word problems”, such as the superman story on page 37. Formalizing such problems in propositional calculus allows us to solve them more easily than we could using English alone.
Fred B. Schneider, David Gries
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