Grigori Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, NATO ASI Series F, pages 289--311. Springer-Verlag, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....occurrences. This technique is derived from structure preserving normal form translations [36, 33] frequently employed in the context of automated deduction (cf. 1] for an overview) We use here a method adapted from a structure preserving translation for intuitionistic logic as described in [26]. Regarding the faithfulness criterion, each of our translations actually satisfies a somewhat stronger condition, referred to as strong faithfulness, expressing that, for any programs and over alphabet A 1 , there is a one to one correspondence between the answer sets of [ and the ....

....1 L 2 ; L 1 L 1 2 ; L 2 L 1 2 ; and 4. if = 1 2 ) then ( consists of the three rules L 1 L 2 L 1 2 ; L 1 2 L 1 ; L 1 2 L 2 : This definition is basically an adaption of a structure preserving normal form translation for intuitionistic logic, as described in [26]. We note at this point that is clearly modular. Furthermore is also polynomial. For the latter property, we provide the following estimations, which can be shown by straightforward induction on the logical complexity of a program. Proposition 7 Let be a nested logic program with n = lc( ....

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G. Mints. Resolution Strategies for the Intuitionistic Logic. In B. Mayoh, E. Tyugu, and J. Penjaam, editors, Constraint Programming: NATO ASI Series, pages 282--304. Springer-Verlag, 1994.

....g) are converted to the form Inh(g) Soundness and completeness proofs of the translation are obtained from the analogous proofs for the fragment F 1 . The most convenient way to 28 extend these proofs is to use the resolution method for intuitionistic logic proposed by G. Mints, see [17] and [18]. In addition to the optimization O 1 , we will apply the analogue of the optimization O 2 to the formula given by the translation T ri. We will further consider the optimization O ap , which is applicable only to the subfragment of F 2 . Definition 6 If t is a composite functional term ap(ap( ....

G. Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, volume 131 of NATO ASI Series F, pages 289-- 311. Springer Verlag, 1994.

....a subformula property, like classical or intuitionistic logic. In the following we will consider resolution calculi for several logics along with suitable search strategies strategies and general properties of the calculi. Detailed analysis of resolution for intuitionistic logic can be found in [9, 14], for linear logic in [8, 13] for modal logic in [15, 10] Descriptions of implemented provers can be found in [13, 14, 15] Different methods for constructing resolution calculi for intuitionistic and multiple valued logics are presented, correspondingly, in [4] in [1] 1.1 Resolution vs The ....

....and maximize the number of contraction applications. It is also important to limit the number of axioms. In particular, we do not want to use an axiom schema which can produce axioms of unrestricted size: A; Gamma A; Delta As an example we bring the intuitionistic sequent calculus GJ from [9] which avoids explicit applications of structural rules. Part of the following material considering the intuitionistic logic is adapted from [14] We present a modification GJm of GJ : Logical axioms. A A for any atom A. Inference rules. A; Gamma D (A B; Gamma ) D B; Gamma D ....

[Article contains additional citation context not shown here]

G. Mints. Resolution Strategies for the Intuitionistic Logic. In Constraint Programming, NATO ASI Series F, v. 131, pp. 289--311, Springer Verlag, (1994).

....logic. For decades, most of the research in automated theorem proving has been concentrated on classical logic. Relatively few papers are devoted on proof search in intuitionistic logic. The following is an incomplete list of such papers: 22] 7] 3] 11] 23] 15] 17] 18] 5] [13]. Despite the fact that several intuitionistic theorem provers have been implemented (see [5] 18] 3] only very few published papers describe the actual implementation of an automated theorem prover and bring the results of running the prover on some benchmarks: 22] and [17] The prover ....

....Calculus When using forward reasoning for proof search it is important to minimize the number of weakening applications and maximize the number of contraction applications: the former increase the size of a derived sequent, the latter decrease it. The intuitionistic sequent calculus GJ from [13] avoids explicit applications of structural rules. We present a modification GJm of GJ : ffl we allow to rename the bound variables. ffl the versions of , 8 and ) which become redundant in the presence of renaming have been dropped. ffl we avoid the special constant denoting absurdity: ....

[Article contains additional citation context not shown here]

G.Mints. Resolution Strategies for the Intuitionistic Logic. In Constraint Programming, NATO ASI Series F, v. 131, pp. 289--311, Springer Verlag, (1994).

....g) are converted to the form Inh(g) Soundness and completeness proofs of the translation are obtained from the analogous proofs for the fragment F 1 . The most convenient way to extend these proofs is to use the resolution method for intuitionistic logic proposed by G. Mints, see [15] and [16]. In addition to the optimization O 1 , we will apply the analogue of the optimization O 2 to the formula given by the translation Tri. We will further consider the optimization O ap , which is applicable only to the subfragment of F 2 . Definition If t is a composite functional term ap(ap( ....

G. Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, volume 131 of NATO ASI Series F, pages 289--311. Springer Verlag, 1994.

....proof may then be transformed to an intuitionistic proof with analytic cuts (without an essential increase of proof length) Secondly, we can translate the input formula into a definitional normal form. Such forms exist for classical as well as for a wide spectrum of non classical logics (see e.g. [1, 9, 6, 15]) If definitions are used in order to abbreviate subformula occurrences then analytic cuts can be simulated even in cut free calculi [2, 3] Now, the procedure is obvious. Translate the formula into definitional form and prove it classically. Then try to get an intuitionistic proof of the ....

....15. Let K k 2 fH k ; D k ; E k g. Then there exists a proof of K k in LJ acut of length 2 d Deltak for some constant d. 5 Structure preserving Translations We start with a review of the translation of closed first order formulae into an intuitionistic normal form. The exposition is based on [6] and [3] Mints introduced this translation in order to provide a normal form for his intuitionistic resolution calculus, but it can also be used with LK and LJ. Indeed, if we apply the definitional translation defined below, it is possible to polynomially simulate analytic cuts. Additionally, we ....

G. Mints. Resolution Strategies for the Intuitionistic Logic. In B. Mayoh, E. Tyugu, and J. Penyam, editors, Constraint Programming, Nato ASI Series, pages 289--311. Springer Verlag, 1994.

....In(t; g) are converted to the form Inh(g) Soundness and completeness proofs of the translation are obtained from the analogous proofs for the fragment F 1 . The most convenient way to extend these proofs is to use the resolution method for intuitionistic logic proposed by G. Mints, see [14] and [15]. In addition to the optimization O 1 , we will apply the analogue of the optimization O 2 to the formula given by the translation T ri. We note that the introduction and elimination rules for disjunction and conjunction can be defined in F 2 . These connectives will be on the different level ....

G. Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, volume 131 of NATO ASI Series F, pages 289--311. Springer Verlag, 1994.

....is a direct extension of the method introduced by Maslov [7] for classical predicate logic. In this way completeness of strategies is first established for the Gentzen type system, and then transferred to resolution. The method is illustrated here for the propositional S4 in a way very similar to [13]. An adaptation of the Maslov s method to S4 and some of the more elaborate strategies mentioned below are presented in [17] Let us recapitulate some material from [10, 11, 12] The main idea of Maslov s method can be summarized as follows: A resolution derivation of the goal clause g from a list ....

G.Mints. Resolution strategies for the intuitionistic logic, Nato ASI Constraint Programming, Springer Lecture Notes in Computer Sci., forthcoming

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Grigori Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, NATO ASI Series F, pages 289--311. Springer-Verlag, 1994.

No context found.

G. Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, pages 289--311. NATO ASI Series F, SpringerVerlag, 1994.

No context found.

G. Mints. Resolution Strategies for the Intuitionistic Logic. In Constraint Programming: NATO ASI Series, pages 282--304. Springer, 1994.

No context found.

Grigori Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, NATO ASI Series F, pages 289--311. Springer-Verlag, 1994.

No context found.

G. Mints. Resolution strategies for the intuitionistic logic. In Constraint Programming, pages 289--311. NATO ASI Series F, SpringerVerlag, 1994.

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