Logical definability of fixed points
نویسندگان
چکیده
منابع مشابه
Minimal predicates, fixed-points, and definability
Minimal predicates P satisfying a given first-order description (P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' (P) which guarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-ord...
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In this article we study interpolation properties for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the -modality easily follow from this result. Furthermore, these properties are extended to the system ILP. Failure of arrow interpolation for ILW is established by providing an explicit count...
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The relationship between counting functions and logical expressibility is explored. The most well studied class of counting functions is #P, which consists of the functions counting the accepting computation paths of a nondeterministic polynomial-time Turing machine. For a logic L, #L is the class of functions on nite structures counting the tuples (T ; c) satisfying a given formula (T ; c) in ...
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We investigate here NP optimization problems from a logical deenability standpoint. We show that the class of optimization problems whose optimum is deenable using rst-order formulae coincides with the class of polynomially bounded NP optimization problems on nite structures. After this, we analyze the relative expressive power of various classes of optimization problems that arise in this fram...
متن کاملGeneralized Rational Relations and their Logical Definability
The family of rational subsets of a direct product of free monoids Σ∗ 1×. . .×Σ ∗ n (the rational relations) is not closed under Boolean operations, except when n = 1 or when all Σi’s are empty or singletons. In this paper we introduce the family of generalized rational subsets of an arbitrary monoid as the closure of the singletons under the Boolean operations, concatenation and Kleene star (j...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1988
ISSN: 0304-3975
DOI: 10.1016/0304-3975(88)90129-6