Results 231 to 240 of about 697,012 (268)

A foray into combinatory logic

Journal of Automated Reasoning, 1986
The paper presents an advocation of the use of automated theorem provers in the area of combinatory logic. The work, inspired by \textit{R. M. Smullyan} [To Mock a Mockingbird (Alfred A. Knopf, New York, 1985)], demonstrates ways of very elegant application of paramodulation theorem proving using system ITP to solving of combinatory logic problems. For
Ross Overbeek
exaly   +3 more sources

Functionality in Combinatory Logic [PDF]

Proceedings of the National Academy of Sciences of the United States of America, 1934
exaly   +4 more sources

Combinatory Logic and the Semantics of Substructural Logics

Studia Logica, 2007
In his earlier paper ``Combinator logics'' [ibid. 76, No. 1, 17--66 (2004; Zbl 1054.03019)] the author extended the positive relevance logic Bo, with and, or and o (fusion) by o-axioms related to the reduction rules of a set of combinators. He then extended the Routley-Meyer semantics to this extended logic.
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A simplification of combinatory logic

Journal of Symbolic Logic, 1972
The usual formulations of combinatory logic, as in Church [1] or Curry and Feys [2], have no straightforward semantics. This lack complicates the proofs of basic metasystematic results, prevents the perspicuous formalization of combinatory logic as a deductive theory, and makes the combinators unnecessarily difficult to apply to recursion theory or to ...
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Asymptotic Properties of Combinatory Logic

2015
We present a quantitative analysis of random combinatory logic terms. Our main goal is to investigate likelihood of semantic properties of random combinators. We show that asymptotically almost all weakly normalizing terms are not strongly normalizing.
Bendkowski, Maciej, Grygiel, Katarzyna, Zaionc, Marek   +2 more
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Combinatory logic with polymorphic types

Archive for Mathematical Logic, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Combinatory logic with discriminators

The Journal of Symbolic Logic, 1970
In this paper, I present a modified and extended version of combinatory logic. Schönfinkel originated the study of combinatory logic (in [2]), but its development is primarily due to H. B. Curry. In the present paper, I will make use of both the symbolism (with some modification) and the results of Curry, as found in [1].What is novel about my version ...
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Categorical combinatory logic

2005
The paper presents the connection between λ-calculus and cartesian closed categories both in an untyped and purely syntactic setting. More specifically we establish a syntactic equivalence theorem between what we call categorical combinatory logic and λ-calculus with explicit products and projections, with β and þ-rules as well as with surjective ...
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Combinatory Logic

1994
Abstract The λ.-calculus was invented in a historical period which was very active for Mathematical Logic. Inspired by Hilbert, many mathematicians were trying to capture the notion of effective calculability. Within the space of ten years the λ.-calculus, Recursive Function Theory and Turing Machines were all invented.
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Combinatory logic

2018
Combinatory logic comprises a battery of formalisms for expressing and studying properties of operations constitutive to contemporary logic and its applications. The sole syntactic category in combinatory logic is that of the applicative term. Closed terms are called ‘combinators’; there is no binding of variables.
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