منابع مشابه
Proofs without syntax
Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition φ as a graph homomorphism h : C → G(φ), where G(φ) is a graph associated with φ and C is a coloured...
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" Mathematicians care no more for logic than logicians for mathematics. " Augustus de Morgan, 1868 Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition ...
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Recent work on word ordering has argued that syntactic structure is important, or even required, for effectively recovering the order of a sentence. We find that, in fact, an n-gram language model with a simple heuristic gives strong results on this task. Furthermore, we show that a long short-term memory (LSTM) language model is even more effective at recovering order, with our basic model out...
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We describe an incremental algorithm for computing interpolants for a pair φA, φB of formulas in propositional logic. In contrast with the common approaches, our method does not require a proof of unsatisfiability of φA ∧ φB , and can be realized using any SAT solver as a black box. We achieve this by combining model enumeration with the ability to easily generate interpolants in the special ca...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2006
ISSN: 0003-486X
DOI: 10.4007/annals.2006.164.1065