Partially ordered connectives and monadic monotone strict np

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 the fragment of SNP whose formulas involve only negative occurrences of relation symbols, only monadic second-order quantifiers, and no occurrences of the equality symbol. It remains an open problem whether MMSNP enjoys the dichotomy property. In the present paper, SNP and MMSNP are characterized in terms of partially ordered connectives. More specifically, SNP is characterized using the logic D of partially ordered connectives introduced in Blass and Gurevich (Annals of Pure and Applied Logic, 32, 1–16, 1986), Sandu and Väänänen (Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 38, 361–372 1992), and MMSNP employing a generalization C of D introduced in the present paper.
Keywords Constraint satisfaction problems  Generalized quantifiers  Henkin quantifiers  MMSNP  Partially ordered connectives  SNP
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DOI 10.1007/s10849-008-9058-5
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References found in this work BETA
On Branching Quantifiers in English.Jon Barwise - 1979 - Journal of Philosophical Logic 8 (1):47 - 80.
Finite Partially-Ordered Quantification.Wilbur John Walkoe Jr - 1970 - Journal of Symbolic Logic 35 (4):535-555.
Henkin Quantifiers and Complete Problems.A. Blass & Y. Gurevich - 1986 - Annals of Pure and Applied Logic 32 (1):1--16.
Finite Partially‐Ordered Quantifiers.Herbert B. Enderton - 1970 - Mathematical Logic Quarterly 16 (8):393-397.
Quantifiers Vs. Quantification Theory.Jaakko Hintikka - 1973 - Dialectica 27 (3‐4):329-358.

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