Arity and alternation in second-order logic
نویسندگان
چکیده
منابع مشابه
Second-order propositional modal logic and monadic alternation hierarchies
We establish that the quantifier alternation hierarchy of formulae of secondorder propositional modal logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs. This solves an open problem problem of van Benthem (1985) and ten Cate (2006). We also identify modal characterizations of the expressive powers of second-order logic (SO) and monadic se...
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for the first time in the history of logic, afzal al-din al-khunaji has found tautologies and contradictories among the verity and actuality propositions. these have been formalized and investigated in first-order logic and it has been shown that their perpetual truth requires the assumption of ‘the presupposed existence of non-existence.’ in this paper, i investigate the tautologies in second-...
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Both firstand second-order logic (FOL and SOL, respectively) as we use them today were arguably created by Frege in his Begriffsschrift – if we ignore the notational differences. SOL also suggests itself as a natural, and because of its much greater strength, desirable extension of FOL. But at least since W. V. Quine’s famous claim that SOL is “set theory in sheep’s clothing” it is widely held ...
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Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison x < y and predicates for x ≡ i mod n has been investigated by Barrington, Compton, Straubing and Thérien. The study of FO[<,MOD]fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1996
ISSN: 0168-0072
DOI: 10.1016/0168-0072(95)00013-5