排序方式: 共有190条查询结果,搜索用时 31 毫秒
21.
In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics. 相似文献
22.
We investigate a contractionless naive set theory, due to Grisin [11]. We prove that the theory is undecidable. 相似文献
23.
In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We then show that for most of the systems under consideration the labelling mechanism can be avoided by choosing an appropriate way of structuring theories. One peculiar feature of our proof systems is the use of restart rules which allow to re-ask the original goal of a deduction. In case of K, K4, S4 and G, we can eliminate such a rule, without loosing completeness. In all the other cases, by dropping such a rule, we get an intuitionistic variant of each system. The present results are part of a larger project of a goal directed proof theory for non-classical logics; the purpose of this project is to show that most implicational logics stem from slight variations of a unique deduction method, and from different ways of structuring theories. Moreover, the proof systems we present follow the logic programming style of deduction and seem promising for proof search [Gabbay and Reyle 84, Miller et al. 91]. 相似文献
24.
Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it. 相似文献
25.
Substructural logics on display 总被引:1,自引:0,他引:1
26.
Lou Goble 《Studia Logica》2004,76(1):17-66
Combinator logics are a broad family of substructual logics that are formed by extending the basic relevant logic B with axioms that correspond closely to the reduction rules of proper combinators in combinatory logic. In the Routley-Meyer relational semantics for relevant logic each such combinator logic is characterized by the class of frames that meet a first-order condition that also directly corresponds to the same combinator's reduction rule. A second family of logics is also introduced that extends B with the addition of propositional constants that correspond to combinators. These are characterized by relational frames that meet first-order conditions that reflect the structures of the combinators themselves. 相似文献
27.
Carlos A. Oller 《Journal of Applied Logic》2004,2(4):451-455
This paper introduces a technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas. The coherence of these sets of formulas is calculated using the minimal models of those sets in G. Priest's Logic of Paradox. The compatibility of the information expressed by a set of formulas with the background or domain knowledge can also be measured with this technique. In this way, Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in)coherence are addressed. 相似文献
28.
A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML+, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML+ based on the recent results for model checking procedures for temporalised logics. TML+ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML+, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments. 相似文献
29.
Sato Kentaro 《Studia Logica》2008,88(2):295-324
We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters.
We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of
-filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters
will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate
which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that
each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery
is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense.
Presented by Wojciech Buszkowski 相似文献
30.
Applied Logic without Psychologism 总被引:1,自引:0,他引:1
Gregory Wheeler 《Studia Logica》2008,88(1):137-156
Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic
may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and
another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception
of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist
view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology
for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference,
including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic
inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. 相似文献