H Andreka, I Hodkinson, and I Nemeti. Finite algebras of relations are representable on nite sets. J. Symbolic Logic, 64:243-267, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....known under the headings relativisation and taming logic . The question which inspired the research reported in this paper is why this relativisation proces turns an undecidable logic into a decidable one. It seems that there are just too many parameters involved to give a general answer. [1] gives a criterion on the truth de nition of modalities being existentially packed which leads on relativised models to decidability and even the nite model property. Such modalities allow the amalgamation of nite structures into loose or tree like models. These last models are also singled ....

....pspace hard satis ability problems. 4 Undecidability by expressing functionality We will show that once we have the possibility to express that a relation is a partial function in arrow logic, the satis ability problem becomes undecidable. A very similar result holds for cylindric modal logic. [1] shows that the arrow logics of the previous section all have the nite base property. This means that none of these logics are strong enough to express that the base of a model is in nite. Square arrow logic has the ability to force 13 Restrictions on universe none re exive symmetric re ....

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H. Andreka, I. Hodkinson, and I. Nemeti. Finite algebras of relations are representable on nite sets. Journal of Symbolic Logic, 64(1):243-267, 1999.

....n 2 this problem becomes exptime complete [7] But of greater importance for our purpose here is that for n = 2, the logic has a special nite model property which gives rise to a straightforward tableau calculus based on labelled deduction ideas. For n 2, the nite model property also holds [1, 6], but a simple model creating technique (like a naive tableau system) does not work (see [9] We designed and implemented a sound and complete labelled tableau calculus for LC 2 , which can be used via the WWW from URL http: www.dcs.kcl.ac.uk cgi bin LC2 lc2.html. We will show how the system ....

....in: 0.35 seconds The next and last example is a countermodel, constructed for the formula 3 23 , which is not a theorem in logic K. Formula: dia a box dia a Parsed formula: vdia (r hcir a) vbox (r hcir vdia (r hcir a) Countermodel: Dom: [0, 1] Valuation: 0 e v(a) Formulas [ dia a in 1, dia a box dia a) in 0, a in 0] Acc. Relation: r(0, 1) r(0, 0) not r(1, 1) not r(1, 0) The input is not a theorem Proof in: 0.383333 seconds. A.3 Statistics The actual version of lc2 has not been designed with ....

H. Andreka, I. Hodkinson, and I. Nemeti. Finite algebras of relations are representable on nite sets. Journal of Symbolic Logic, 64:243-267, 1999.

....fragments is even in Exptime, in fact Exptime complete. Gr a99] also establishes the nite model property for GF, using a technique which involves the so called Herwig s Theorem which was rst employed by Andr eka, Hodkinson and N emeti to show the nite model property for similar fragments, AHN99] What is more, GF has a certain tree model property, ABN98] Since the tree model property of the modal fragment can be seen as the main reason behind the robustness of the decidability of that fragment (cf. e.g. Var98] this gives hope as to the robustness of GF. And indeed, adding least ....

H. Andreka, I. Hodkinson, and I. Nemeti. Finite algebras of relations are representable on nite sets. Journal of Symbolic Logic, 64:243-267, 1999.

....[41] de ned a pspace complete guarded fragment with the nite tree model property. This fragment satis es both locality principles. The nite model property for the guarded and several subfragments of the packed fragment was established in an algebraic setting by Andr eka, Hodkinson N emeti [1]. Gr adel [21] provides a direct proof for the guarded fragment. At the time of writing (spring 2000) I. Hodkinson announced a proof for the nite model property for the full packed fragment. All these results are based on variants of a result due to Herwig [29] The use of Herwig s Theorem to ....

H. Andreka, I. Hodkinson, and I. Nemeti. Finite algebras of relations are representable on nite sets. Journal of Symbolic Logic, 64(1):243-267, 1999.

....elements but does not have any nite square relativised representation. We remark that with respect to a slightly di erent notion of n square relativised representation, the answer to the problem is positive for all n; this can be shown by Herwig s theorem [Her95, Her98b] using techniques of [AHN99] Here is a vague question. Consider the following evidence: CRA 3 and CRA 4 are elementary, consisting of the atomic algebras in RA n ; a similar result holds for boolean algebras. But for n 5, CRA n is not elementary; a similar result holds for RRA. RA 3 and RA 4 are nitely ....

H Andreka, I Hodkinson, and I Nemeti. Finite algebras of relations are representable on nite sets. J. Symbolic Logic, 64:243-267, 1999.

....elements but does not have any nite square relativised representation. We remark that with respect to a slightly di erent notion of n square relativised representation, the answer to the problem is positive for all n; this can be shown by Herwig s theorem [Her95, Her98b] using techniques of [AHN99] Here is a vague question. Consider the following evidence: CRA 3 and CRA 4 are elementary, consisting of the atomic algebras in RA n ; a similar result holds for boolean algebras. But for n 5, CRA n is not elementary; a similar result holds for RRA. RA 3 and RA 4 are nitely ....

H Andreka, I Hodkinson, and I Nemeti. Finite algebras of relations are representable on nite sets. J. Symbolic Logic, 64:243-267, 1999.

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H. Andreka, I. Hodkinson, and I. Nemeti. Finite algebras of relations are representable on nite sets. Journal of Symbolic Logic, 64:243-267, 1999.

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