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Fixed point logics

Anuj Dawar & Yuri Gurevich

Bulletin of Symbolic Logic 8 (1):65-88 (2002)

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Many-Valued Logic, Partiality, and Abstraction in Formal Specification Languages.Reiner Hähnle - 2005 - Logic Journal of the IGPL 13 (4):415-433.details The purpose of this article is to clarify the role that many-valued logic can or should play in formal specification of software systems for modeling partiality. We analyse a representative set of specification languages. Our findings suggest that many-valued logic is less useful for modeling those aspects of partiality, for which it is traditionally intended: modeling non-termination and error values. On the other hand, many-valued logic is emerging as a mainstream tool in abstraction of formal analyses of various kinds, and (...) Download Export citation Bookmark
Expressiveness and definability in circumscription.Francicleber Martins Ferreira & Ana Teresa Martins - 2011 - Manuscrito 34 (1):233-266.details We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is Δ-elementary, then it is elementary. That is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. This means that classes of (...) Download Export citation Bookmark
Expressive equivalence of least and inflationary fixed-point logic.Stephan Kreutzer - 2004 - Annals of Pure and Applied Logic 130 (1-3):61-78.details We study the relationship between least and inflationary fixed-point logic. In 1986, Gurevich and Shelah proved that in the restriction to finite structures, the two logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivalent to any LFP-formula was left open.In this paper, we answer the question negatively, i.e. we show that the two logics are equally expressive on arbitrary structures. We give a syntactic translation of IFP-formulae to LFP-formulae (...) Download Export citation Bookmark 4 citations
Symbioses between mathematical logic and computer science.Andreas Blass - 2016 - Annals of Pure and Applied Logic 167 (10):868-878.details Download Export citation Bookmark
ŁΠ logic with fixed points.Luca Spada - 2008 - Archive for Mathematical Logic 47 (7-8):741-763.details We study a system, μŁΠ, obtained by an expansion of ŁΠ logic with fixed points connectives. The first main result of the paper is that μŁΠ is standard complete, i.e., complete with regard to the unit interval of real numbers endowed with a suitable structure. We also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real closed (...) Download Export citation Bookmark 2 citations

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