D. Basin, S. Matthews and L. Vigano. Labelled modal logics: quantifiers. J. of Logic, Language and Information, 7(3);237--263, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....represents a generic possibility accessible from . The more general study of such sys tems has put them in a new proof theoretic perspective recently. They are closely related to semantics based translation systems [Ohlbach, 1991, Nonnengart, 1993] and labelled deductive systems [Gabbay, 1996, Basin et al. 1998] I use the term explicitly scoped from [Stone, 1999] because I continue to emphasize the extent to which the two formulations of reasoning represent the same inferences, just in different ways. The ability to define explicit scope is intimately connected with the ability to carry out ....

.... treatment of the first order modal logic using prefix terms and analytic tableaux (or, seen upside down, in the cut free sequent calculus) of [Fitting and Mendelsohn, 1998] I factor out reasoning about accessibility into side conditions on inference rules, similar to the proof theoretic view of [Basin et al. 1998], in which reasoning about accessibility and boolean reasoning are clearly distinguished. And I use Herbrand terms to reason correctly about parameterized instances of formulas, avoiding the usual eigenvariable condition on quantifier (and modal) rules, as in [Lincoln and Shankar, 1994] Though ....

Basin, D., Matthews, S., and Vigano, L. (1998). Labelled modal logics: Quantifiers. Journal of Logic, Language and Information, 7(3):237--263.

.... with prefixed tableaux [Fitting, 1983] the logical foundation of Herbrand terms [Lincoln and Shankar, 1994] and the possibilities for enforcing a proof theoretic separation in modal deduction between constraints on accessibility and general first order reasoning [Frisch and Scherl, 1991, Basin et al. 1998] SCL has the advantage that inferences can be freely interchanged, allowing arbitrary proofs to be transformed easily into goal directed proofs we show in Theorem 1, presented in Section 4.2, how to obtain goal directed proofs in this calculus. The very same flexibility of inference, however, ....

Basin, D., Matthews, S., and Vigano, L. (1998). Labelled modal logics: Quantifiers. Journal of Logic, Language and Information, 7(3):237--263.

....reasoning processes on a subset of the global knowledge. Some formalisms have been proposed for the representation and integration of distributed knowledge and reasoning systems. The most important are based on Multi Modal Logics [9] 1 Labelled Deductive Systems (LDS) and LDS for Modal Logics [6, 1], Annotated Logics [17] and Cooperative Information Systems [4] The underlying idea of these formalisms is that the truth values of certain formulae in different knowledge subsystems are related one another. In modal logics axioms relating different modal operators and constraints between ....

....knowledge and reasoning. Labelled Deductive Systems, Modal Logics, Annotated Logics, and Cooperative Information Systems. In the following we compare them with DFOL. LDS [10] are very general logical systems. We therefore compare DFOL with the family of LDSs for Quantified Modal Logics (LDSQML) [1]. LDSQMLs deal with domains and relations between domains, as well as relations between formulae. LDSQMLs provide a formalization for modal logics with varying, increasing, decreasing, and constant domains. The main analogies between FOML and LDSQML is that they both allow distinct domains, and ....

D. Basin, S. Matthews, and L. Vigan`o. Labelled Modal Logics: Quantifiers. Journal of Logic, Language and Information, 1998. To Appear.

....67 1 Thanks to Mark Steedman, Rich Thomason and L. Thorne McCarty for extensive comments. This work was supported by a postdoctoral fellowship from RUCCS. November 9, 1999. 2 1 Introduction Recent years have seen an explosion in research in formalizing inference in modal logic [Gore, 1999, Basin et al. 1998, Fitting and Mendelsohn, 1998] and in using modal theories in knowledge representation [Fagin et al. 1995, McCarthy and Buvac, 1994, Stone, 1998] Unfortunately, research on modal inference does not link up as directly as could be hoped with proposed modal theories. This report aims to help ....

....these choices are familiar from research on modal logic. For example, Fitting and Mendelsohn, 1998] present a comprehensive treatment of the first order modal logic using prefix terms and analytic tableaux. But they treat FIRST ORDER MULTI MODAL DEDUCTION 3 only a single modal operator. [Basin et al. 1998] adopt a proof theoretic view of first order modal logic in which reasoning about accessibility and boolean reasoning are clearly distinguished. But they also treat only a single modal operator, and do so using atomic terms for worlds and natural deduction proof. Meanwhile, Baldoni et al. 1998] ....

Basin, D., Matthews, S., and Vigano, L. (1998). Labelled modal logics: Quantifiers. Journal of Logic, Language and Information, 7(3):237--263.

....Kripke semantics, and are thus equivalent to the corresponding Hilbert systems only when these are themselves complete with respect to the same semantics. Due to lack of space, discussions and proofs have been omitted or considerably shortened; a detailed account is given in our technical report [3]. Furthermore, here we do not discuss proof theoretic results and implementational aspects, but point out that (i) the proof theoretic results for labelled PMLs carry over to QMLs, so that proof search may be restricted (normal proofs have the subformula property) and the effectiveness of theorem ....

.... thus allow the formalization of all quantified modal logics) first order logic, or some subset thereof We showed in [4] that there are tradeoffs in formalization: different choices require different formalizations of the base modal logic and have different metatheoretic properties (see also [3]) In [4] we settled on those logics with an accessibility relation axiomatizable in terms of Horn clauses, a choice we repeat here. We choose to admit precisely those properties of R that can be formulated by a collection of relational rules, i.e. Horn) rules of the form p1 R q1 Delta Delta ....

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D. Basin, S. Matthews, and L. Vigan`o. Labelled modal logics: quantifiers. Technical Report MPI-I-97-2-001, MPI fur Informatik, Saarbrucken, 1997.

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D. Basin, S. Matthews and L. Vigano. Labelled modal logics: quantifiers. J. of Logic, Language and Information, 7(3);237--263, 1998.

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D. Basin, S. Matthews, and L. Vigan`o. Labelled Modal Logics: Quantifiers. Journal of Logic, Language and Information, 1998. To Appear.

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D. Basin, S. Matthews, and L. Vigan`o. Labelled Modal Logics: Quantifiers. Journal of Logic, Language and Information, 1998. To Appear.

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