E. Gradel. Why are modal logics so robustly decidable? Bulletin EATCS, 68:90-103, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for bisimulation invariant logics can moreover be pinpointed with translations into emptiness problems for suitable treeautomata. As Vardi argues in [24] the tree model property (rather than the nite model property) accounts for the robust decidability of logics for the modal domain (also compare [9]) Unravellings, however, rarely work for the purpose of nite model theory, simply because any unravelling of a transition system with directed cycles will be in nite; indeed, acyclicity and niteness are mutually exclusive in bisimilar companions of any system with directed cycles. In section ....

E. Gr adel, Why are modal logics so robustly decidable?, Bulletin of the European Association for Theoretical Computer Science, vol. 68 (1999), pp. 90-103.

....point. Through the standard or relational translation, modal languages may be viewed as fragments of rst order languages [3] Modal fragments are computationally very wellbehaved; their satis ability and model checking problems are of reasonably low complexity, and they are so in a robust way [16, 8]. The guarded fragment [1] was introduced as a generalization of the modal fragment, one that retains the good computational properties of modal fragments as much as possible. On top of that, good computational behavior of modal and guarded fragments has been explained in terms of the tree model ....

E. Gradel. Why are modal logics so robustly decidable? Bulletin EATCS, 68:90-103, 1999.

.... such abstractions are those for the calculus (see e.g. the well founded pre models in [SE89] We will show that each SIM model can be unravelled into a Hintikka tree, and thus prove a tree model property for SIM (such properties are known to be helpful for the decidability of modal logics [Gr a99] This section is the core of the paper since it combines the preliminary results from the previous sections with the ideas underlying the introduction of Hintikka trees. For a SIM formula, a Hintikka tree for is labelled with symbolic states, has a dummy root node, and, at its rst level, ....

E. Gradel. Why are modal logics so robustly decidable? Bulletin of the EATCS, 68:90-103, 1999.

.... of either FO2 or the guarded fragment that is decidable and such that GSP(REG) can be naturally translated into it We already know that the satis ability problem of every regular grammar logic can be translated into satis ability for the guarded xed point logic LGF 44 that is in EXPTIME [Gr a99b] when the relation symbols have bounded arity. Indeed, PDL can be translated into the modal calculus and the modal calculus can be translated in polynomial time into LGF . The design of a simple polynomial time transformation from GSP(REG) into satis ability for LGF is open (for instance ....

E. Gradel. Why are modal logics so robustly decidable? Bulletin of the EATCS, 68:90-103, 1999.

.... in ExpTime or even PSpace and NP (see e.g. 19, 1 More recently it has been argued that some modal phenomena are better explained by their tree model property [28] i.e. they are determined by tree like structures) and or by embedding them in bounded (or guarded) fragments of rst order logic [1, 13]. The logics we consider here do not have those properties. 2, 25] the two variable fragment is NExpTime complete [14] A question naturally arising is why modal logics, in general, are of a lower complexity than the two variable fragment. It is worth noting that this phenomenon is not due to ....

E. Gradel. Why are modal logics so robustly decidable? Bulletin of the European Association for Theoretical Computer Science, 68:90-103, 1999.

....latter are fragments of the former. In contrast, more recently, it has been argued that some modal phenomena are better explained by their treemodel property [25] i.e. they are determined by tree like structures) and or by embedding them in bounded (or guarded) fragments of rst order logic [1, 13]. Many of the above observations apply to standard description logics as well. The relationship between rst order logic and description logics was rst investigated by Borgida who identi es several DLs that are fragments of FO 2 and even presents a description logic D that is as expressive as ....

E. Gradel. Why are modal logics so robustly decidable? Bull. of the Eur. Assoc. for Theoretical Computer Science, 68:90-103, 1999.

.... in ExpTime or even PSpace and NP (see e.g. 19, 1 More recently it has been argued that some modal phenomena are better explained by their tree model property [29] i.e. they are determined by tree like structures) and or by embedding them in bounded (or guarded) fragments of rst order logic [1, 13]. The logics we consider here do not have those properties. 2, 26] the two variable fragment is NExpTime complete [14] A question naturally arising is why modal logics, in general, are of a lower complexity than the two variable fragment. It is worth noting that this phenomenon is not due to ....

E. Gradel. Why are modal logics so robustly decidable? Bulletin of the European Association for Theoretical Computer Science, 68:90-103, 1999.

....procedure that fully exploits the special nature of the resulting rst order fragment. 3 3 The Tree Model Property In recent years, the tree model property has been identi ed as one of the semantic key features explaining the good logical and computational behavior of many modal logics; see [Gr a99,Var97] for two accessible presentations. De nition 2. A tree T is a relational structure (T ; S) where T , the set of nodes, contains a unique r 2 T (called the root) such that 8t 2 T (S rt) every element of T distinct from r has a unique S predecessor; and S is acyclic; that is, 8t ....

E. Gradel. Why are modal logics so robustly decidable? Bulletin EATCS, 68:90-103, 1999.

....of DT L reg , an initial formal model of XSL. They did not consider ecient versions of MSO or connections with logics with path expressions. Guarded fragments of rst order and xpoint logic have been mainly investigated w.r.t. the explanation of decidability questions of various modal logics [17]. Very little work has been devoted to the complexity of their model checking problem. We mention Alechina and Immerman [6] who de ned a guarded transitive closure logic admitting linear time model checking. A crucial difference with the above mentioned guarded logics is that we consider trees ....

E. Gradel. Why are modal logics so robustly decidable ? Bulletin of the European Association for Theoretical Computer Science, 68:90-103, 1999.

.... structures of arbitrary vocabulary and still would retain convenient features of modal logic, such as the characterization via an appropriate notion of bisimulation, the applicability of automata based methods, and the good balance between expressiveness and algorithmic manageability (see [13]) Syntactically, guarded logics are based on a restriction of rst order quanti cation to the form 9y( x; y) x; y) or 8y( x; y) x; y) where quanti ers may range over a tuple y of variables, but are guarded by a formula that must contain all the free variables of the formula that ....

E. Gr adel, Why are modal logics so robustly decidable?, in Current Trends in Theoretical Computer Science. Entering the 21st Century, G. Paun, G. Rozenberg, and A. Salomaa, eds., World Scientic, 2001, 393-498.

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E. Gradel. Why are modal logics so robustly decidable? Bulletin EATCS, 68:90-103, 1999.

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E. Gradel. Why are modal logics so robustly decidable? Bulletin of the European Association for Theoretical Computer Science. EATCS, 68:90-103, 1999.

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E. Gr adel, Why are modal logics so robustly decidable?, Bulletin of the European Association for Theoretical Computer Science 68 (1999), pp. 90-103.

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