Henkin and function quantifiers

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Henkin and Function Quantifiers

Henkin [7] introduced quantifiers which arise when usual (universal and existential) quantifiers are arranged in non-linear order. These quantifiers bre known as partially ordered quantifiers or Henkin quantifiers. Is. was observed already in [7] that languages with these quantifiers are stronger than first-order logic. A result of [ll] shows that even the weakest enkin quantifier has essential...

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Henkin quantifiers and complete problems

Certain applications of logic to computer science, for example those discus: in [4], have the following features: only finite models are of interest, first-order logic is not sufficiently expressive. Accordingly, various extensions first-order logic have been proposed and analyzed for finite structures. " analysis often reveals connections with computational complexity, and ind some of the exte...

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Decidability Problems in Languages with Henkin Quantifiers

Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 (1992) 149-172. We consider the language L(H,) with all Henkin quantifiers H, defined as follows: H,,x,...x,y,.~.y, 4(x,,..., x,, Y,, . , Y,) iff 3f, . . .f, Vxx, . . .x, 9(x,, . . ,x,, f,(xA . , f,(x,)). We show that the theory of equality in L(H,) is undecidable. The ...

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Henkin quantifiers and Boolean formulae: A certification perspective of DQBF

Article history: Received 16 October 2012 Received in revised form 4 November 2013 Accepted 20 December 2013 Communicated by N. Shankar

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Degrees of logics with Henkin quantifiers in poor vocabularies

We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L∗∅ is of degree 0 . We show that the same holds also for some weaker logics like L∅(Hω) and L∅(Eω). We...

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ژورنال

عنوان ژورنال: Annals of Pure and Applied Logic

سال: 1989

ISSN: 0168-0072

DOI: 10.1016/0168-0072(89)90071-7