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Switch to: References
Citations of:
Henkin Quantifiers
In Michał Krynicki, Marcin Mostowski & Lesław W. Szczerba (eds.), Quantifiers: Logics, Models and Computation: Volume Two: Contributions. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 193--263 (1995)
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Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension $L_{*}^{1}$ (H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close $L_{*}^{1}$ (H) with respect to Boolean operations, and obtain the language L¹(H). At the next level, we consider an extension $L_{*}^{2}$ (H) of L¹(H) in which every sentence is an L¹(H)-sentence prefixed with (...) |
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We introduce several senses of the principle ofcompositionality. We illustrate the difference between them with thehelp of some recent results obtained by Cameron and Hodges oncompositional semantics for languages of imperfect information. |
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This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically (...) |
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The examination of quantifiers plays an essential role in modern linguistic theories. One of the most important issues in this respect was raised by Jaakko Hintikka, who proposed the following thesis: Certain natural language sentences require essential non-linear quantification to adequately express their logical form. |
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This volume presents mathematical game theory as an interface between logic and philosophy. |
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Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation. |
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This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ‘moving pictures of thought’. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...) |
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The often observed complexity gap between the expressiveness of a logical formalism and its exponentially harder expression complexity is proven for all logical formalisms which satisfy natural closure conditions. The expression complexity of the prefix classes of second-order logic can thus be located in the corresponding classes of the weak exponential hierarchies; further results about expression complexity in database theory, logic programming, nonmonotonic reasoning, first-order logic with Henkin quantifiers and default logic are concluded. The proof method illustrates the significance of (...) |
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Motivated by constraint satisfaction problems, Feder and Vardi (SIAM Journal of Computing, 28, 57–104, 1998) set out to search for fragments of satisfying the dichotomy property: every problem definable in is either in P or else NP-complete. Feder and Vardi considered in this connection two logics, strict NP (or SNP) and monadic, monotone, strict NP without inequalities (or MMSNP). The former consists of formulas of the form , where is a quantifier-free formula in a relational vocabulary; and the latter is (...) |
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