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681.
682.
This paper presents a new modal logic for ceteris paribus preferences understood in the sense of “all other things being equal”. This reading goes back to the seminal work of Von
Wright in the early 1960’s and has returned in computer science in the 1990’s and in more abstract “dependency logics” today.
We show how it differs from ceteris paribus as “all other things being normal”, which is used in contexts with preference defeaters. We provide a semantic analysis and
several completeness theorems. We show how our system links up with Von Wright’s work, and how it applies to game-theoretic
solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary
modal logics. 相似文献
683.
We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations
of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising
and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number
of predicates in the overlying language.
Supported by a UK Engineering and Physical Sciences Research Council (EPSRC) Research Studentship. 相似文献
684.
Ulrich Meyer 《Journal of Philosophical Logic》2009,38(2):229-247
According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified
tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use
of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now”
and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not
be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does
not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of
the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic. 相似文献
685.
C. M. Asmus 《Journal of Philosophical Logic》2009,38(4):405-431
In this paper I present a range of substructural logics for a conditional connective ↦. This connective was original introduced
semantically via restriction on the ternary accessibility relation R for a relevant conditional. I give sound and complete proof systems for a number of variations of this semantic definition.
The completeness result in this paper proceeds by step-by-step improvements of models, rather than by the one-step canonical
model method. This gradual technique allows for the additional control, lacking in the canonical model method, that is required. 相似文献
686.
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
687.
688.
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
689.
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
690.
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