共查询到20条相似文献,搜索用时 15 毫秒
1.
Olivia Caramello 《Mathematical Logic Quarterly》2014,60(4-5):335-347
We investigate the problem of characterizing the classes of Grothendieck toposes whose internal logic satisfies a given assertion in the theory of Heyting algebras, and introduce natural analogues of the double negation and De Morgan topologies on an elementary topos for a wide class of intermediate logics. 相似文献
2.
Rosalie Iemhoff 《Archive for Mathematical Logic》2006,45(5):581-599
If the Visser rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How
to characterize the admissible rules of intermediate logics for which not all of the Visser rules are admissible is not known.
In this paper we give a brief overview of results on admissible rules in the context of intermediate logics. We apply these
results to some well-known intermediate logics. We provide natural examples of logics for which the Visser rule are derivable,
admissible but nonderivable, or not admissible.
Supported by the Austrian Science Fund FWF under projects P16264 and P16539. 相似文献
3.
Marcus Kracht 《Mathematical Logic Quarterly》1993,39(1):301-322
A logic Λ bounds a property P if all proper extensions of Λ have P while Λ itself does not. We construct logics bounding finite axiomatizability and logics bounding finite model property in the lattice of intermediate logics and in the lattice of normal extensions of K4.3. MSC: 03B45, 03B55. 相似文献
4.
Rosalie Iemhoff 《Indagationes Mathematicae》2019,30(3):470-491
The skolem class of a logic consists of the formulas for which the derivability of the formula is equivalent to the derivability of its Skolemization. In contrast to classical logic, the skolem classes of many intermediate logics do not contain all formulas. In this paper it is proven for certain classes of propositional formulas that any instance of them by (independent) predicate sentences in prenex normal form belongs to the skolem class of any intermediate logic complete with respect to a class of well-founded trees. In particular, all prenex sentences belong to the skolem class of these logics, and this result extends to the constant domain versions of these logics. 相似文献
5.
S. Mojtaba Mojtahedi 《Mathematical Logic Quarterly》2014,60(1-2):6-11
Let denote a first‐order logic in a language that contains infinitely many constant symbols and also containing intuitionistic logic . By , we mean the associated logic axiomatized by the double negation of the universal closure of the axioms of plus . We shall show that if is strongly complete for a class of Kripke models , then is strongly complete for the class of Kripke models that are ultimately in . 相似文献
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Jeroen P. Goudsmit 《Archive for Mathematical Logic》2014,53(7-8):779-808
Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics in terms of their admissible rules. To illustrate the technique, we also provide a refutation system for Medvedev’s logic. 相似文献
8.
Christian Espíndola 《Archive for Mathematical Logic》2013,52(7-8):823-826
We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisting of instances of the principle of excluded middle for sentences (REM). We prove that both schemata combined derive classical logic, while each one of them provides a strictly weaker intermediate logic, and neither of them is derivable from the other. We show that over every intermediate logic there exists a maximal intermediate logic for which Glivenko’s theorem holds. We deduce as well a characterization of DNS, as the weakest (with respect to derivability) scheme that added to REM derives classical logic. 相似文献
9.
《Annals of Pure and Applied Logic》2022,173(10):103143
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete for all intermediate inquisitive and dependence logics. To this end, we define inquisitive and dependence algebras and we investigate their model-theoretic properties. We then focus on finite, core-generated, well-connected inquisitive and dependence algebras: we show they witness the validity of formulas true in inquisitive algebras, and of formulas true in well-connected dependence algebras. Finally, we obtain representation theorems for finite, core-generated, well-connected, inquisitive and dependence algebras and we prove some results connecting team and algebraic semantics. 相似文献
10.
Alexander Citkin 《Archive for Mathematical Logic》2012,51(1-2):1-14
With any structural inference rule A/B, we associate the rule ${(A \lor p)/(B \lor p)}$ , providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( ${\lor}$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a ${\lor}$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the ${\lor}$ -extension of each admissible rule is admissible. We prove that any structural finitary consequence operator (for intermediate logic) can be defined by a set of ${\lor}$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. 相似文献
11.
Pierangelo Miglioli 《Archive for Mathematical Logic》1992,31(6):415-432
Summary Infinitely many intermediate propositional logics with the disjunction property are defined, each logic being characterized both in terms of a finite axiomatization and in terms of a Kripke semantics with the finite model property. The completeness theorems are used to prove that any two logics are constructively incompatible. As a consequence, one deduces that there are infinitely many maximal intermediate propositional logics with the disjunction property. 相似文献
12.
In this paper, we propose some decision logic languages for rule representation in rough set-based multicriteria analysis. The semantic models of these logics are data tables, each of which is comprised of a finite set of objects described by a finite set of criteria/attributes. The domains of the criteria may have ordinal properties expressing preference scales, while the domains of the attributes may not. The validity, support, and confidence of a rule are defined via its satisfaction in the data table. 相似文献
13.
W. Pohlers 《Archive for Mathematical Logic》1991,30(5-6):311-376
In the first part we show why ordinals and ordinal notations are naturally connected with proof theoretical research. We introduce the program of ordinal analysis. The second part gives examples of applications of ordinal analysis.Dedicated to K. Schütte on the occasion of his 80th birthdayWork partly supported by a grant of the Volkswagenstiftung 相似文献
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V.V. Rybakov 《Archive for Mathematical Logic》2003,42(2):179-200
In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound
and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for
knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe
their connections and give dividing examples. Also we find algorithms recognizing these properties for some particular cases.
Received: 21 October 2000 / Published online: 2 September 2002
Key words or phrases: Multi-agent systems – Non-standard logic – Knowledge representation – Common knowledge – Common information – Fixed points,
Kripke models – Modal logic 相似文献
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Siegfried Gottwald 《Fuzzy Sets and Systems》1980,3(2):181-192
Fuzzy logic ∞9 considered in connection with fuzzy sets theory, is a special theory, is a special many valued logic with truth-value sets [0, 1], which has been studied already by Lukasiewicz. We consider also his versions m for m ? 2 with finite truth-value sets. In all cases we add two further propositional connectives, one conjunction and one disjunction. For these logics we give a list of tautologies, consider relations between their sets of tautologies, prove their compactness, and mention some further results. 相似文献
18.
Norihiro Kamide 《Mathematical Logic Quarterly》2007,53(3):219-225
A mechanism for combining any two substructural logics (e.g. linear and intuitionistic logics) is studied from a proof‐theoretic point of view. The main results presented are cut‐elimination and simulation results for these combined logics called synthesized substructural logics. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
We investigate the expressivity of many-valued modal logics based on an algebraic structure with a complete linearly ordered lattice reduct. Necessary and sufficient algebraic conditions for admitting a suitable Hennessy–Milner property are established for classes of image-finite and (appropriately defined) modally saturated models. Full characterizations are obtained for many-valued modal logics based on complete BL-chains that are finite or have the real unit interval [0, 1] as a lattice reduct, including ?ukasiewicz, Gödel, and product modal logics. 相似文献
20.
《International Journal of Approximate Reasoning》2008,49(3):766-783
We introduce a general framework that is based on distance semantics and investigate the main properties of the entailment relations that it induces. It is shown that such entailments are particularly useful for non-monotonic reasoning and for drawing rational conclusions from incomplete and inconsistent information. Some applications are considered in the context of belief revision, information integration systems, and consistent query answering for possibly inconsistent databases. 相似文献