I Hodkinson, Loosely guarded fragment of first-order logic has the finite model property, Studia Logica (2001), to appear. See http://www.doc.ic.ac.uk/~imh/papers/lgf.ps.gz  Home/Search   Document Details and Download   Summary   Related Articles   Check

....8x t2T t(x) ht;ci2T con t(c) is equivalent to a fluted sentence. But this is almost obvious: by only renaming variables in formulas from sub x , we can rewrite all of them as fluted (classical) formulas over X 1 with at most one free variable x 1 . 2 10 As was observed by I. Hodkinson (see [7]) Theorem 74 of [8] can be extended to the loosely guarded fragment introduced in [12] Definition 18 (loosely guarded fragment) Denote by T LGF the smallest set of T L formulas such that ffl every atomic formula is in T LGF ; ffl if and are in T LGF , then so are , S , U , fl , ....

....is a conjunct of fl containing both x and y, then 9y(fl ) 2 T LGF . The set T LGF is called the loosely guarded fragment of the first order temporal language. Using the fact that the loosely guarded fragment of classical first order logic is decidable [12, 6] and has the finite model property [7], and following the proof of Theorem 74 of [8] one can readily prove the following Theorem 19. Let F and F be as in Theorem 17. Then the fragments TL(F) T L 1 T LGF and TL fin (F ) T L 1 T LGF are decidable. Acknowledgments We are grateful to R. Schmidt, A. Degtyarev, I. ....

I. Hodkinson. Loosely guarded fragment of first-order logic has the finite model property. Manuscript, Imperial College London, 2000.

....2] Using theorem 12 and the arguments of [6, theorem 36, corollary 37] it suffices to show that it is decidable whether a state candidate S is finitely realizable. But S is finitely realizable iff a S (as in lemma 15) has a finite model. The packed fragment has the finite model property [4, 5], so this is iff a S has a model. The result now follows from the decidability of the packed fragment. 2 Remark 16 Since the packed fragment has the finite model property, any realizable state candidate is finitely realizable. However, not every satisfiable monodic packed sentence is true in some ....

I Hodkinson, Loosely guarded fragment of first-order logic has the finite model property, Studia Logica (2001), to appear. See http://www.doc.ic.ac.uk/~imh/papers/lgf.ps.gz

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