Making knowledge explicit: How hard it is

Brezhnev, V. S.; Kuznets, Roman

doi:10.1016/j.tcs.2006.03.010

Cited by 43 publications

(15 citation statements)

References 3 publications

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“…However, the authors of Ref. [4] note that, since S4-decision is PSPACE-complete, it may be the case that the S4-derivation of A is exponential, in which case the LP-derivation of A r , or some LP-formula in it (including A r itself), may be exponential with respect to |A|; this is consistent with Lemma 4.17.…”

Section: Fact 51 [Realization Theorem]supporting

confidence: 61%

“…4 We show that E respects the restrictions of evidence functions; due to C-analycity, only terms occurring in have to be considered. (5) and (6) obtain T ω.n|t ·s A, which closes with (4).…”

Section: Analytic Methods For the Logic Of Proofs 13mentioning

confidence: 88%

“…• A result by Brezhenv and Kuznets, in which a relation between LP theorems can be computed from S4 proofs in polynomial time [4].…”

Section: Related Workmentioning

confidence: 99%

“…This result was greatly improved by Brezhnev and Kuznets [4], by presenting a realization algorithm in which the size of the LP-derivation of A r , and of every term occurring in it, is polynomial on the size of the S4-derivation of A. However, the authors of Ref.…”

Section: Fact 51 [Realization Theorem]mentioning

confidence: 99%

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Analytic Methods for the Logic of Proofs

Finger

2008

Journal of Logic and Computation

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The logic of proofs (LP) was proposed as Gödel's missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for LP have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for LP that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of LP-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

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Section: Fact 51 [Realization Theorem]supporting

confidence: 61%

Section: Analytic Methods For the Logic Of Proofs 13mentioning

confidence: 88%

“…• A result by Brezhenv and Kuznets, in which a relation between LP theorems can be computed from S4 proofs in polynomial time [4].…”

Section: Related Workmentioning

confidence: 99%

Section: Fact 51 [Realization Theorem]mentioning

confidence: 99%

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Analytic Methods for the Logic of Proofs

Finger

2008

Journal of Logic and Computation

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“…for every k the set T (k) = {l|Prf(k, l)} is finite. 7 3. Proofs can be joined into longer proofs; i.e.…”

Section: Arithmetical Interpretation Of Lpv − and Lpvmentioning

confidence: 99%

An Arithmetical Interpretation of Verification and Intuitionistic Knowledge

Protopopescu

2015

Logical Foundations of Computer Science

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Intuitionistic epistemic logic introduces an epistemic operator, which reflects the intended BHK semantics of intuitionism, to intuitionistic logic. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based, thereby providing the systems of intuitionistic epistemic logic extended by an epistemic operator based on verification with an arithmetical semantics too.

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On Two Models of Provability

Artëmov

Mathematical Problems From Applied Logic II

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Making knowledge explicit: How hard it is

Cited by 43 publications

References 3 publications

Analytic Methods for the Logic of Proofs

Analytic Methods for the Logic of Proofs

An Arithmetical Interpretation of Verification and Intuitionistic Knowledge

On Two Models of Provability

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