The theorem prover of the program verifier Tatzelwurm

Käufl, Thomas; Zabel, Nicolas

doi:10.1007/3-540-52885-7_128

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…More challenging would be a setting where rules are added to the knowledge base that generate new terms if they find a certain constellation in the knowledge base (e.g., a married couple, for which the rule introduces a ground term denoting the couple and assertions that the couple with its components). In the context of first-order logic and modal logics, the combination of tableau-based reasoning and congruence closure has respectively been investigated in [9] and [14].…”

Section: Discussionmentioning

confidence: 99%

Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols

Baader

Kapur

2020

Automated Reasoning

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The word problem for a finite set of ground identities is known to be decidable in polynomial time, and this is also the case if some of the function symbols are assumed to be commutative. We show that decidability in P is preserved if we also assume that certain function symbols f are extensional in the sense that f (s1, . . . , sn) ≈ f (t1, . . . , tn) implies s1 ≈ t1, . . . , sn ≈ tn. In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.

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Section: Discussionmentioning

confidence: 99%

Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols

Baader

Kapur

2020

Automated Reasoning

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Deciding the Word Problem for Ground and Strongly Shallow Identities w.r.t. Extensional Symbols

Baader

Kapur

2022

J Autom Reasoning

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The word problem for a finite set of ground identities is known to be decidable in polynomial time using congruence closure, and this is also the case if some of the function symbols are assumed to be commutative or defined by certain shallow identities, called strongly shallow. We show that decidability in P is preserved if we add the assumption that certain function symbols f are extensional in the sense that $$f(s_1,\ldots ,s_n) \mathrel {\approx }f(t_1,\ldots ,t_n)$$ f ( s 1 , … , s n ) ≈ f ( t 1 , … , t n ) implies $$s_1 \mathrel {\approx }t_1,\ldots ,s_n \mathrel {\approx }t_n$$ s 1 ≈ t 1 , … , s n ≈ t n . In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.

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The theorem prover of the program verifier Tatzelwurm

Cited by 2 publications

References 3 publications

Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols

Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols

Deciding the Word Problem for Ground and Strongly Shallow Identities w.r.t. Extensional Symbols

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