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691.
We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted
behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability
of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including
non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to
the standard approach, while also bringing a new algebraic perspective to logics which are algebraizable using the standard
tools of AAL. Furthermore, we pave the way toward a robust behavioral theory of AAL, namely by providing a behavioral version
of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several well-known characterization
results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach.
Presented by Daniele Mundici 相似文献
692.
693.
We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle. 相似文献
694.
Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion
is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order
logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic
and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable
in polynomial time), although by means of growing computational resources, and converge towards classical propositional logic.
The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of
Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies
all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator)
while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict
sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion
of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational
complexity are associated with the depth at which the use of virtual information is allowed. 相似文献
695.
We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of
each others’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variable-forgetting
as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation,
it follows that beliefs not involving the forgotten atom(s) remain true.
The work for this publication was mainly carried out while Hans van Ditmarsch was associated to: Institut de Recherche en
Informatique, Université Paul Sabatier, France. 相似文献
696.
Mehrnoosh Sadrzadeh 《Synthese》2009,167(2):391-408
What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? How much can we weaken and still be able to reason about multi-agent scenarios in a tidy compositional way? This paper provides some answers. 相似文献
697.
We introduce a deontic action logic and its axiomatization. This logic has some useful properties (soundness, completeness, compactness and decidability), extending the properties usually associated with such logics. Though the propositional version of the logic is quite expressive, we augment it with temporal operators, and we outline an axiomatic system for this more expressive framework. An important characteristic of this deontic action logic is that we use boolean combinators on actions, and, because of finiteness restrictions, the generated boolean algebra is atomic, which is a crucial point in proving the completeness of the axiomatic system. As our main goal is to use this logic for reasoning about fault-tolerant systems, we provide a complete example of a simple application, with an attempt at formalization of some concepts usually associated with fault-tolerance. 相似文献
698.
WANG Lu 《Frontiers of Philosophy in China》2008,3(1):83-98
Research into logical syntax provides us the knowledge of the structure of sentences, while logical semantics provides a window
into uncovering the truth of sentences. Therefore, it is natural to make sentences and truth the central concern when one
deals with the theory of meaning logically. Although their theories of meaning differ greatly, both Michael Dummett’s theory
and Donald Davidson’s theory are concerned with sentences and truth and developed in terms of truth. Logical theories and
methods first introduced by G. Frege underwent great developments during the past century and have played an important role
in expanding these two scholars’ theories of meaning.
Translated by Ma Minghui from Zhexue Yanjiu 哲学研究 (Philosophical Research), 2006, (7): 53–61 相似文献
699.
López-Astorga Miguel 《Frontiers of Philosophy in China》2016,11(2):279-297
Johnson-Laird and Byrne distinguished ten kinds of conditionals. Their framework was the mental models theory and they attributed different combinations of semantic possibilities to those ten types of conditionals. Based on such combinations, the mental models theory has clear predictions for reasoning tasks, including those kinds of conditionals and involving reasoning schemata such as Modus Ponens, Modus Tollens, the affirming the consequent fallacy, and the denying the antecedent fallacy. My aim in this paper is to show that the predictions of the mental logic theory for those reasoning tasks are exactly the same as those of the mental models theory, and that, therefore, such tasks are not useful to decide which of the two theories is correct. 相似文献
700.
Philippe Balbiani Andreas Herzig Nicolas Troquard 《Journal of Philosophical Logic》2008,37(4):387-406
We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also
provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity
operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s
STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula
without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both
for the deliberative and Chellas’s STIT. 相似文献