Combining Syntax and Semantics through Prime Form Representation

Bittencourt, Guilherme

doi:10.1093/logcom/exm051

Cited by 13 publications

(7 citation statements)

References 25 publications

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“…Let A be a set of finite pointed L ✷ -action models, that is, a set containing pointed L ✷ -action models (thus with precondition and postconditions functions returning formulas in L ✷ ) whose domain is finite (non-empty) and in which each action affects the truth-value of at most a finite number of atomic propositions. 4 The language L ✷A extends L ✷ with new formulas of the form The set of valid formulas of L ✷A is denoted by Log ✷A .…”

Section: A Simpler 'Forgetting' Actionmentioning

confidence: 99%

Forgetting complex propositions

et al. 2015

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This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition π is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this.We resolve this situation by considering expressions of the form [ ‡π]ϕ, which quantify over all possible (but 'minimal') ways of forgetting whether π. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets π (rather than forgets whether π) and when the modification of atomic facts is done non-uniformly throughout the model.

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Section: A Simpler 'Forgetting' Actionmentioning

confidence: 99%

Forgetting complex propositions

et al. 2015

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“…This is why prime implicates are considered an interesting target language for knowledge compilation (Cadoli & Donini, 1997;Darwiche & Marquis, 2002). Prime implicates have also proved relevant to other sub-areas of AI, like distributed reasoning (Adjiman, Chatalic, Goasdoué, Rousset, & Simon, 2006), belief revision (Bittencourt, 2007;Pagnucco, 2006), non-monotonic reasoning (cf. Przymusinski, 1989), and characterizations of relevance (Lakemeyer, 1995;Lang, Liberatore, & Marquis, 2003).…”

Section: Introductionmentioning

confidence: 99%

Prime Implicates and Prime Implicants: From Propositional to Modal Logic

Bienvenu

2009

jair

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Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be appropriately extended from propositional logic to the modal logic K. We begin the paper by considering a number of potential definitions of clauses and terms for K. The different definitions are evaluated with respect to a set of syntactic, semantic, and complexity-theoretic properties characteristic of the propositional definition. We then compare the definitions with respect to the properties of the notions of prime implicates and prime implicants that they induce. While there is no definition that perfectly generalizes the propositional notions, we show that there does exist one definition which satisfies many of the desirable properties of the propositional case. In the second half of the paper, we consider the computational properties of the selected definition. To this end, we provide sound and complete algorithms for generating and recognizing prime implicates, and we show the prime implicate recognition task to be Pspace-complete. We also prove upper and lower bounds on the size and number of prime implicates. While the paper focuses on the logic K, all of our results hold equally well for multi-modal K and for concept expressions in the description logic ALC.

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“…1 Clauses are often referred to as sets of literals. An implicate of a formula is a clause entailed by the formula, and a non-tautological clause is a prime implicate if no proper subset is an implicate.…”

Section: Preliminariesmentioning

confidence: 99%

“…Numerous algorithms have been developed to compute prime implicates -see, for example, [1,2,3,5,6,8,9,12,14,18,19]. Most use clause sets or truth tables as input, but rather few allow arbitrary formulas, such as the pi-trie algorithm introduced in [10].…”

Section: Introductionmentioning

confidence: 99%

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Trie Based Subsumption and Improving the pi-Trie Algorithm

Matusiewicz

Murray²,

Rosenthal³

EPiC Series in Computing

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An algorithm that stores the prime implicates of a propositional logical formula in a trie was developed in [10]. In this paper, an improved version of that pi-trie algorithm is presented. It achieves its speedup primarily by significantly decreasing subsumption testing. Preliminary experiments indicate the new algorithm to be substantially faster and the trie based subsumption tests to be considerably more efficient than the clause by clause approach originally employed.

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Combining Syntax and Semantics through Prime Form Representation

Cited by 13 publications

References 25 publications

Forgetting complex propositions

Forgetting complex propositions

Prime Implicates and Prime Implicants: From Propositional to Modal Logic

Trie Based Subsumption and Improving the pi-Trie Algorithm

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