Results 11 to 20 of about 201,623 (302)
Open Higher-Order Logic. [PDF]
, 2023 We introduce a variation on Barthe et al.’s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity, differentiability, or monotonicity, can be expressed and reasoned about in a very natural way, following the structure of ...
Ugo Dal Lago +2 more
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CERES in higher-order logic [PDF]
Annals of Pure and Applied Logic, 2011 Cut-elimination by resolution (CERES) for first-order logic [\textit{M. Baaz} et al., Lect. Notes Comput. Sci. 3452, 481--495 (2005; Zbl 1108.03305)] transforms the set of cut-formulas in a given proof \(\pi\) into a refutable formula \(R\). Given a resolution refutation of \(R\), cuts are sufficiently easily eliminated from \(\pi\).
Stefan Hetzl +2 more
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Refinement of Higher-Order Logic Programs [PDF]
, 2003 A refinement calculus provides a method for transforming specifications to executable code, maintaining the correctness of the code with respect to its specification. In this paper we extend the refinement calculus for logic programs to include higher-order programming capabilities in specifications and programs, such as procedures as terms and lambda ...
Robert Colvin +3 more
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Extensional Higher-Order Logic Programming [PDF]
ACM Transactions on Computational Logic, 2010 We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixed-
Angelos Charalambidis +3 more
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A theorem proving framework for the formal verification of Web Services Composition [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 We present a rigorous framework for the composition of Web Services within a higher order logic theorem prover. Our approach is based on the proofs-as-processes paradigm that enables inference rules of Classical Linear Logic (CLL) to be translated into ...
Petros Papapanagiotou +1 more
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Embedding of Quantified Higher-Order Nominal Modal Logic into Classical Higher-Order Logic
EPiC Series in Computing, 2018 In this paper, we present an embedding of higher-order nominal modal logicinto classical higher-order logic, and study its automation. There exists no automated theorem prover for first-order or higher-order nominal logic at the moment, hence, this is the first automation for this kind of logic.In our work, we focus on nominal tense logic and have ...
Wisniewski, Max, STEEN, Alexander
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Taking Stock: Hale, Heck, and Wright on Neo-Logicism and Higher-Order Logic [PDF]
, 2021 Four philosophical concerns about higher-order logic in general and the specific demands placed on it by the neo-logicist project are distinguished.
Wright, Crispin
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Superposition for Full Higher-order Logic [PDF]
, 2021 AbstractWe recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free$$\lambda $$λ-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism ...
Alexander Bentkamp +3 more
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Extensional Semantics for Higher-Order Logic Programs with Negation [PDF]
Logical Methods in Computer Science, 2018 We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [Bezem99,Bezem01] for positive higher-order programs.
Panos Rondogiannis, Ioanna Symeonidou
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Grundlagen §64: an alternative strategy to account for second-order abstraction
Principia: An International Journal of Epistemology, 2022 A famous passage in Section 64 of Frege’s Grundlagen may be seen as a justification for the truth of abstraction principles. The justification is grounded in the procedure of content recarving which Frege describes in the passage.
Vincenzo Ciccarelli
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