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771.
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
772.
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
773.
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
774.
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
775.
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
776.
Terrance W. Klein 《Zygon》2006,41(2):365-380
Abstract. For many in the Anglo‐American tradition of language analysis, Ludwig Wittgenstein, the great progenitor of twentieth‐century philosophy of language, showed conclusively that theological terms lack any referent in reality and therefore represent a discourse that can do no more than manifest the existential attitudes that speakers take toward reality as a whole. To think that such terms represent more is to be bewitched by the use of language. Is it possible, however, that theological language references a fundamental human drive? In this article I reexamine the dyad of nature and supernature from the perspective of Wittgenstein's philosophy. Perhaps surprisingly, Wittgenstein's thought on the subject offers much more than his famous, terse aphorism at the conclusion of his first masterwork, the Tractatus Logico‐Philosophicus ([1921] 1961, 74, §7): “What we cannot speak about we must pass over in silence.” Furthermore, the basic Tractarian drive to determine the relationship between language and reality, which is redirected but not extinguished in Wittgenstein's second, divergent, opus, the Philosophical Investigations ([1953] 1967), may be the place for a renewed examination of what the supernatural means in human discourse. Does talk of God give expression to the fundamental transcendence of human knowledge? Is it a language game we can eschew? 相似文献
777.
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
778.
The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of
propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class
of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed
under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological
Kripke-style models for logics that are sound and complete with respect to varieties of distributive lattices with operators
in the above-mentioned classes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
779.
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
780.