Construction and learnability of canonical Horn formulas
نویسندگان
چکیده
منابع مشابه
Canonical Ground Horn Theories
An abstract framework of canonical inference based on proof orderings is applied to ground Horn theories with equality. A finite presentation that makes all normal-form proofs available is called saturated. To maximize the chance that a saturated presentation be finite, it should also be contracted, in which case it is deemed canonical. We apply these notions to propositional Horn theories – or...
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1 Background Rewrite rules are oriented equations used to replace equals-by-equals in the speciied direction. Input terms are repeatedly rewritten according to the rules. When and if no rule applies, the resultant normal form is considered the value of the initial term. If no innnite sequences of rewrites is possible, a rewrite system is said to have the termination property. Connuence of a rew...
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We generalize the theory of canonical formulas for K4 (the logic of transitive frames) to wK4 (the logic of weakly transitive frames). Our main result establishes that each logic over wK4 is axiomatizable by canonical formulas, thus generalizing Zakharyaschev’s theorem for logics over K4. The key new ingredients include the concepts of transitive and strongly cofinal subframes of weakly transit...
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We introduce a new graph parameter, the hydra number, arising from the minimization problem for Horn formulas in propositional logic. The hydra number of a graph G = (V, E) is the minimal number of hyperarcs of the form u, v → w required in a directed hypergraph H = (V, F ), such that for every pair (u, v), the set of vertices reachable in H from {u, v} is the entire vertex set V if (u, v) ∈ E,...
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Dependency quantified Boolean formulas (DQBF ) extend quantified Boolean formulas with Henkin-style partially ordered quantifiers. It has been shown that this is likely to yield more succinct representations at the price of a computational blow-up from PSPACE to NEXPTIME. In this paper, we consider dependency quantified Horn formulas (DQHORN ), a subclass of DQBF, and show that the computationa...
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ژورنال
عنوان ژورنال: Machine Learning
سال: 2011
ISSN: 0885-6125,1573-0565
DOI: 10.1007/s10994-011-5248-5