Results 21 to 30 of about 131,879,682 (302)
Logical Methods in Computer Science, 2014 The Stone tautologies are known to have polynomial size resolution refutations and require exponential size regular refutations. We prove that the Stone tautologies also have polynomial size proofs in both pool resolution and the proof system of regular ...
Samuel R. Buss +1 more
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The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems [PDF]
Logical Methods in Computer Science, 2015 We investigate wether three statements in analysis, that can be proved classically, are realizable in the realizability model of extensional continuous functionals induced by Kleene's second model $K_2$.
Dag Normann
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Representations of measurable sets in computable measure theory [PDF]
Logical Methods in Computer Science, 2014 This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly countably ...
Klaus Weihrauch +1 more
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On the Unusual Effectiveness of Logic in Computer Science [PDF]
Bulletin of Symbolic Logic, 2001 In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”.
Halpern, Joseph Y. +5 more
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Admissibility in Finitely Generated Quasivarieties [PDF]
Logical Methods in Computer Science, 2013 Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable ...
George Metcalfe +1 more
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The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in \Bbb N$ [PDF]
Logical Methods in Computer Science, 2018 We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, do form a directed complete partial ordering.
Dag Normann
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On Small Types in Univalent Foundations [PDF]
Logical Methods in Computer Science, 2023 We investigate predicative aspects of constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle.
Tom de Jong, Martín Hötzel Escardó
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Proofs as stateful programs: A first-order logic with abstract Hoare triples, and an interpretation into an imperative language [PDF]
Logical Methods in Computer ScienceWe introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare logic, and the ...
Thomas Powell
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Continuous Regular Functions [PDF]
Logical Methods in Computer Science, 2020 Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function $f:[0,1] \to [0,1]$ is $r$-regular if there is a B\"{u}chi automaton that accepts precisely the set of base $r \in \mathbb{N}$ representations of elements of the graph of $f$.
Alexi Block Gorman +7 more
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Tameness in least fixed-point logic and McColm's conjecture [PDF]
Logical Methods in Computer Science, 2021 We investigate four model-theoretic tameness properties in the context of least fixed-point logic over a family of finite structures. We find that each of these properties depends only on the elementary (i.e., first-order) limit theory, and we completely
Siddharth Bhaskar, Alex Kruckman
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