Natural deduction as higher-order resolution
نویسندگان
چکیده
منابع مشابه
Natural Deduction as Higher-Order Resolution
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause. Resolution gives both forwards and backwards proof, supporting a large class of logics. Isabelle has been used to prove theorems in Martin-Löf’s C...
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We present a proof-searching algorithm for the classical first order natural deduction calculus and prove its correctness. For any given task (if this task is indeed solvable), a searching algorithm terminates, either finding a corresponding natural deduction proof or giving a set of constraints, from which a counter-example can be extracted. Proofs of the properties which characterize correctn...
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The logic behind parsers for categorial grammars can be formalized in several different ways. Lambek Calculus (LC) constitutes an example for a natural deduction 1 style parsing method. In natural language processing, the task of a parser usually consists in finding derivations for all different readings of a sentence. The original Lambek Calculus, when it is used as a parser / theorem prover, ...
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The introduction of sorts to rst-order automated deduction has brought greater conciseness of representation and a considerable gain in eeciency by reducing the search space. It is therefore promising to treat sorts in higher order theorem proving as well. In this paper we present a generalization of Huet's Constrained Resolution to an order-sorted type theory T with term declarations. This sys...
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This is a companion paper to [6] where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geom...
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ژورنال
عنوان ژورنال: The Journal of Logic Programming
سال: 1986
ISSN: 0743-1066
DOI: 10.1016/0743-1066(86)90015-4