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An Algorithmic Approach to Recover Inconsistent Knowledge-bases - Arieli (1919) (Correct)
....of malfunction devices, and database management systems that amalgamate distributed knowledge bases. 1 Motivation In this paper we introduce an algorithmic approach to revise inconsistent information and restore its consistency. This approach (sometimes called coherent [5] or conservative [15]) considers contradictory data as useless, and uses only a consistent part of the original information for making inferences. To see the rationality behind this approach consider, for instance, the following set of propositional assertions: KB = fp; p; pq; r; rsg: Since :p is true in KB, so ....
G.Wagner. Vivid logic. Springer-Verlag, LNAI No.764, 1994.
Explicit Provability and Constructive Semantics - Artemov (2000) (1 citation) (Correct)
.... truth explicit, though informal, by introducing what is now known as the Brouwer Heyting Kolmogorov (BHK) semantics ( 48] 49] 52] The BHK semantics is widely recognized as the intended semantics for intuitionistic logic ( 30] 31] 38] 56] 67] 71] 94] 95] 97] 98] [101], 104] Its description uses the unexplained primitive notions of construction and proof (Kolmogorov used the term problem solution for the latter) It stipulates that ffl a proof of AB consists of a proof of A and a proof of B, Received by the editors September 14, 1998; revised August 11 of ....
, Logic and structure, Springer-Verlag, 1994.
The Logic of Provability - Japaridze, de Jongh (1998) (13 citations) (Correct)
....A 2 T , and 2A 2B 2 T implies 2A 2 T or 2B 2 T ) Note that faithfully interpretable theories in a finite number of propositional variables are necessarily r.e. The theorem was given a more compact proof and at the same time generalized to all r.e. theories extending I Delta 0 EXP by Zambella [1994]. If one applies the theorem to the minimal L propositional theory, an earlier proved strengthening of Solovay s theorem (Artemov [1980] Avron [1984] Boolos [1982] Montagna [1979] Visser [1980] rolls out. 5.2. Corollary. Uniform arithmetic completeness theorem) There exists a sequence of ....
....of PA) The logic of the provability predicate of HA with regard to HA certainly contains additional principles beyond the obvious intuitionistic version of L: the intuitionistic propositional calculus IPC plus 2(2A A) 2A. The situation has been discussed by Visser in several papers (Visser [1985,1994], Visser et al. 1995] It is unknown what the real logic is, for all we know it may even be complete Pi 0 2 . In any case it contains the additional principles: ffl 2: 2A 22A ffl 2( 2A 2A) 22A ffl 2(A B) 2(A 2B) Leivant s Principle 2 ) But this is not an exhaustive list. It ....
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Logic and Structure, Springer Verlag, Berlin, Amsterdam. L. L. Esakia
Four-Valued Logics for Reasoning with Uncertainty in Prioritized.. - Arieli (1999) (Correct)
....Proof: For instance, p; q j= W q, but p; q; q 6j= W q. 2 The proof of the last proposition also shows that j= W is not reflexive. 5 However, in many reasoning systems (especially those for drawing nontrivial conclusions from inconsistent data) reflexivity is not valid in general (see, e.g. [15, 19]) Still, as it clearly follows from Proposition 3.12 below, j= W is reflexive w.r.t. premises that are true in every possible world setting: Definition 3.11 Con(KB) T fS j S2W(KB)g. Proposition 3.12 Let be a clause that does not contain any atomic formula and its negation. If Con(KB) j= 4 ....
G.Wagner. Vivid logic. LNAI 764. Springer-Verlag, 1994. 12
The Logic of Provability - Japaridze, de Jongh (1997) (13 citations) (Correct)
....A 2 T , and 2A 2B 2 T implies 2A 2 T or 2B 2 T ) Note that faithfully interpretable theories in a finite number of propositional variables are necessarily r.e. The theorem was given a more compact proof and at the same time generalized to all r.e. theories extending I Delta 0 EXP by Zambella [1994]. If one applies the theorem to the minimal L propositional theory, an earlier proved (Artemov [1980] Avron [1984] Boolos [1982] Montagna [1979] Visser [1980] strengthening of Solovay s theorem rolls out. 5.2. Corollary. Uniform arithmetic completeness theorem) There exists a sequence of ....
....I Sigma k but with the induction for Sigma k formulas formulated as a rule. The corresponding provability logic can be axiomatized over CSM by the Pi 1 essential reflexivity schema 4A 4(2(A S) S) where S is as before. We also know two natural provability logics of type A (Beklemishev [1994]) The first system corresponds to pairs of theories (T; U) such that U is an extension of T by finitely many Pi 1 sentences and proves times iterated consistency of T , such as e.g. the pairs (PA; PA Con(ZF) I Sigma 1 ; I Sigma 1 Con(I Sigma 2 ) etc. This logic can be axiomatized ....
[Article contains additional citation context not shown here]
Logic and Structure, Springer Verlag, Berlin. L. L. Esakia
Chapter Vii - The Logic Of (1968) (1 citation) (Correct)
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Logic and Structure, Springer Verlag, Berlin, Amsterdam. L. L. Esakia
Explicit Provability And Constructive Semantics - Artemov (2001) (1 citation) (Correct)
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, Logic and structure, Springer-Verlag, 1994.
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