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51.
In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed. 相似文献
52.
Wojciech Buszkowski 《Studia Logica》2007,87(2-3):145-169
We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars.
The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system
of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid.
Special Issue Categorial Grammars and Pregroups Edited by
Wojciech Buszkowski and Anne Preller 相似文献
53.
Marta Bílková 《Studia Logica》2007,85(1):1-31
We investigate uniform interpolants in propositional modal logics from the proof-theoretical point of view.
Our approach is adopted from Pitts’ proof of uniform interpolationin intuitionistic propositional logic [15]. The method is
based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus
for which structural rules are admissible.
We shall present such a proof of the uniform interpolation theorem for normal modal logics K and T. It provides an explicit
algorithm constructing the interpolants.
Presented by Heinrich Wansing 相似文献
54.
We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke's semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the deduction theorem. By means of a Henkin argument strong completeness is proved making use of predicate logical principles, which are only classically acceptable. 相似文献
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56.
We investigate sequent calculi for the weak modal (propositional) system reduced to the equivalence rule and extensions of it up to the full Kripke system containing monotonicity, conjunction and necessitation rules. The calculi have cut elimination and we concentrate on the inversion of rules to give in each case an effective procedure which for every sequent either furnishes a proof or a finite countermodel of it. Applications to the cardinality of countermodels, the inversion of rules and the derivability of Löb rules are given. 相似文献
57.
Clare Marie Moriarty 《British Journal for the History of Philosophy》2018,26(3):429-451
This paper responds to two issues in interpreting George Berkeley’s Analyst. First, it explains why the text contains no discussion of religious mysteries or points of faith, despite the claims of the text's subtitle; I argue that the subtitle must be understood, and its success assessed, in conjunction with material external to the text. Second, it’s unclear how naturally the arguments of the Analyst sit with Berkeley’s broader views. He criticizes the methodology of calculus and conceptually problematic entities, and the extent to which they require one to bend the rules of classical mathematics. Yet, elsewhere, Berkeley’s opinion of classical mathematics and its intelligibility is low, and he defends a pragmatic approach to word meaning that should not find fault with so functionally successful a theory. The ad hominem intention of the text makes it difficult to discern to what extent Berkeley is committed to the sincerity of these criticisms. This component of the text is rarely discussed, but I argue that when trying to decide what Berkeley’s true position is in the Analyst, we should treat its ad hominem component as its primary intention. 相似文献
58.
Professor H. Neudecker 《Psychometrika》1981,46(3):343-345
The author provides a full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion. He uses matrix differential calculus in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented. 相似文献
59.
Gerard A. W. Vreeswijk 《Argumentation》1995,9(2):305-342
Defeasible reasoning is concerned with the logics of non-deductive argument. As is described in the literature, the study of this type of reasoning is considerably more involved than the study of deductive argument, even so that, in realistic applications, there is often a lack of resources to perform an exhaustive analysis. It follows that, in a theory of defeasible reasoning, the order and direction in which arguments are developed, i.e. theprocedure, is important. The aim of this article is to show that debate is the most efficient procedure to argue in the presence of limited resources. To do so, there is first some general theory on defeasible argumentation, which is followed by an introduction to the problem of dialectical search. The problem of dialectical search is (or at least, should be) the essential issue in every theory on argumentation, and emerges at every occasion that involves adjudication on competing arguments. Starting with an example, it is explained that dialectical search can be best scheduled according to classical debating techniques, that work along well-tried methods. These methods (which include various forms of curtailment, interruption, and interpretation) have proven their value in keeping debating efforts within reasonable bounds. How they apply in a theory of formal argument, will be shown in this article.This research was made possible by SION, and is financed by NWO under contract number 612-316-019. Part of this research has been conducted at the Vrije Universiteit Amsterdam. This article contains fragments of Chapter 6 and Chapter 7 of the author's dissertation. Studies in Defeasible Argumentation (1993). 相似文献
60.