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841.
We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits
a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart
of Tarski’s quasi-projective relation algebras.
Supported by the Hungarian National Foundation for Scientific Research grant T73601. 相似文献
842.
José Ferreirós 《Synthese》2009,170(1):33-70
David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom). 相似文献
843.
844.
Edwin D. Mares 《Synthese》2009,167(2):343-362
This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic
71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian
truth condition holds for universally quantified statements, their information condition is quite different. The information
condition utilizes general propositions. The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an
adequate theory of general information. 相似文献
845.
The logic of how-questions 总被引:1,自引:0,他引:1
William Jaworski 《Synthese》2009,166(1):133-155
Philosophers and scientists are concerned with the why and the how of things. Questions like the following are so much grist for the philosopher’s and scientist’s mill: How can we be free and yet live in a deterministic universe?, How do neural processes give rise to conscious experience?, Why does conscious experience accompany certain physiological events at all?, How is a three-dimensional perception of depth generated by a pair of two-dimensional retinal images?. Since Belnap and Steel’s pioneering work on the logic of questions, Van Fraassen has managed to apply their approach in constructing an account of the logic of why-questions. Comparatively little, by contrast, has been written on the logic of how-questions despite the apparent centrality of questions such as How is it possible for us to be both free and determined? to philosophical enterprise.1 In what follows I develop a logic for how-questions of various sorts including how-questions of cognitive resolution, how-questions of manner, how-questions of method, of means, and of mechanism. 相似文献
846.
将一个图形(称为母图)的若干条线段删除后得到的图形叫做母图的子图。运用实验方法探讨了子图结构学习和子图变式学习对解决问题的迁移效果。结果表明:子图结构学习仅对解决“图形结构相同、逻辑结构相同”问题有明显迁移作用;子图变式学习对解决“图形结构相同、逻辑结构相同”没有明显迁移作用,对“图形结构相似、逻辑结构相同”、“图形结构相同、逻辑结构相似”以及“图形结构相似、逻辑结构相似”四类问题均有明显迁移作用。 相似文献
847.
848.
Paolo Liberatore 《Studia Logica》2007,86(1):89-110
A consistency default is a propositional inference rule that asserts the consistency of a formula in its consequence. Consistency
defaults allow for a straightforward encoding of domains in which it is explicitely known when something is possible. The
logic of consistency defaults can be seen as a variant of cumulative default logic or as a generalization of justified default
logic; it is also able to simulate Reiter default logic in the seminormal case. A semantical characterization of consistency
defaults in terms of processes and in terms of a fixpoint equation is given, as well as a normal form.
Presented by Melvin Fitting 相似文献
849.
Jan Plaza 《Synthese》2007,158(2):165-179
Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static
states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper
(part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with
public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results
and formulate a general method that solves certain kind of problems involving public communications—among them well known
puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction
of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics.
This paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer,
M. Hadzikadic, & Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems:
Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24. Research partly supported by NSF Grant CCR-8702307
and PSC-CUNY Grant 668283. 相似文献
850.
Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny.
There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research
community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive
reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are
interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic
systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations
of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of
symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal
Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive
explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes
a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both
approaches employ standard neural network architectures which are already known to be highly effective in practical learning
applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning
in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning,
while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world.
Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to
learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective
of symbolic and sub-symbolic integration.
相似文献
John WoodsEmail: |