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731.
Petr Hájek 《Studia Logica》2006,84(1):51-62
Important works of Mostowski and Rasiowa dealing with many-valued logic are analyzed from the point of view of contemporary mathematical fuzzy logic.A version of this paper has been presented during the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005. 相似文献
732.
In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic.A preliminary version of this paper was presented at the fifth conference on Advances in Modal Logic (AiML 2004) in Manchester. We would like to thank Maarten Marx for his comments on an early draft and Agnieszka Kisielewska for help with the proof reading.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen 相似文献
733.
Maxwell J. Cresswell 《Studia Logica》2006,82(3):307-327
The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given
classical prepositional logic, one can easily prove that every consistent set of propositions can be embedded in a ‘maximal
consistent set’, which in a sense represents a possible world. However the construction depends on the fact that standard
modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite subset of which
is intuitively ‘possible’ in natural language has the property that the whole set is possible. The argument of the paper is
that the principles needed to shew that natural language possibility sentences involve quantification over worlds are analogous
to those used in infinitary modal logic. 相似文献
734.
Larisa Maksimova 《Studia Logica》2006,82(2):271-291
Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena
Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large
families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply
powerful machinery of universal algebra.
In this paper we present an overview of results on interpolation and definability in modal and positive logics,and also in
extensions of Johansson's minimal logic. All these logics are strongly complete under algebraic semantics. It allows to combine
syntactic methods with studying varieties of algebras and to flnd algebraic equivalents for interpolation and related properties.
Moreover, we give exhaustive solution to interpolation and some related problems for many families of propositional logics
and calculi.
This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.
Presented by Jacek Malinowski 相似文献
735.
Josep Maria Font 《Studia Logica》2006,82(2):179-209
This paper reviews the impact of Rasiowa's well-known book on the evolution of algebraic logic during the last thirty or forty
years. It starts with some comments on the importance and influence of this book, highlighting some of the reasons for this
influence, and some of its key points, mathematically speaking, concerning the general theory of algebraic logic, a theory
nowadays called Abstract Algebraic Logic. Then, a consideration of the diverse ways in which these key points can be generalized
allows us to survey some issues in the development of the field in the last twenty to thirty years. The last part of the paper
reviews some recent lines of research that in some way transcend Rasiowa's approach. I hope in this way to give the reader
a general view of Rasiowa's key position in the evolution of Algebraic Logic during the twentieth century.
This paper is an extended version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.
Presented by Jacek Malinowski 相似文献
736.
Jeffrey S. Olson 《Studia Logica》2006,83(1-3):393-406
CRS(fc) denotes the variety of commutative residuated semilattice-ordered monoids that satisfy (x ⋀ e)k ≤ (x ⋀ e)k+1. A structural characterization of the subdi-rectly irreducible members of CRS(k) is proved, and is then used to provide a
constructive approach to the axiomatization of varieties generated by positive universal subclasses of CRS(k).
Dedicated to the memory of Willem Johannes Blok 相似文献
737.
In this paper, we define a family of fuzzy hybrid logics that are based on Gödel logic. It is composed of two infinite-valued versions called and , and a sequence of finitary valued versions . We define decision procedures for both and that are based on particular sequents and on a set of proof rules dealing with such sequents. As these rules are strongly invertible the procedures naturally allow one to generate countermodels. Therefore we prove the decidability and the finite model property for these logics. Finally, from the decision procedure of , we design a sound and complete sequent calculus for this logic. 相似文献
738.
Contemporary studies in unconscious cognition are essentially founded on dissociation, i.e., on how it dissociates with respect to conscious mental processes and representations. This is claimed to be in so many and diverse ways that one is often lost in dissociation. In order to reduce this state of confusion we here carry out two major tasks: based on the central distinction between cognitive processes and representations, we identify and isolate the main dissociation paradigms; we then critically analyze their key tenets and reported findings. 相似文献
739.
Mark T. Nelson 《Argumentation》1995,9(4):553-562
Since the time of David Hume, many philosophers have held that there is a logical Is/Ought gap. According to the doctrine of the Is/Ought gap, there are no valid (i.e., non-fallacious) arguments from purely factual premises about whatis the case to moral or normative conclusions about whatought to be. Occasionally, this doctrine has been challenged, but frequently it has been accepted without argumentation. Charles Pigden has recently argued for a logical Is/Ought gap on the grounds of the conservativeness of logic. I offer a counter-example which shows that Pigden's argument is unsound and that there need be no logical gap between Is-premises and an Ought-conclusion. My counter-example is an argument which is logically valid, has only Is-premises and an Ought-conclusion, and does not purport to violate the conservativeness of logic. Moreover, my argument does not rely, as other alleged counter-examples do, on controversial assumptions from Aristotelian biology about natures or ends, or about institutions such as promise-making. 相似文献
740.
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