G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita degli Studi di Roma \La Sapienza", 1995. Home/Search Document Details and Download
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A Modal Perspective on Path Constraints - Alechina, Demri, de Rijke (2003) (4 citations) (Correct)
....iroot. The node rt is the only node w in G satisfying G; w j= root. Hence, our symbol root is an example of a so called nominal (a proposition letter that is true of at most a single node of a model) PDL with converse is called converse PDL (CPDL) We obtain CPDL with nominals (see e.g. [20]) by extending CPDL with nominals. 3.2 De ning the Logic PDL The logic PDL we study is a fragment of CPDL with nominals augmented with the wildcard #. Here s a more precise de nition. De nition 5 (PDL ) The path expressions of PDL considered are those introduced in De nition 1 with ....
....interpreted by a singleton. This is not quite true because of the presence of #, but we will show below that it is correct when non deterministic L structures are considered (see the proof of Theorem 11) Hence, modulo the presence of #, PDL can be viewed as a fragment of CPDL with nominals [20] or as a fragment of the hybrid calculus [43] Furthermore, the constructive calculus introduced in [5] also contains nominals (i.e. proposition letters interpreted by singletons) as well as a form of recursion. We don t need the full expressive power of the calculus, however: we are ....
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G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita degli Studi di Roma \La Sapienza", 1995.
The Complexity of Regularity in Grammar Logics - Demri (2001) (1 citation) (Correct)
....(see also [Hem94] The study of the complexity of PDL like logics (e.g. the modal calculus, Combinatory PDL) can be understood as the modal counterpart for the study of decidable fragments of second order logic. Indeed, many modal logics can be naturally embedded into PDL like logics (see e.g. [Tuo90, Sch91, Gia95]) and therefore the design of ecient decision procedures for PDL like logics is another way to study the complexity of modal logics in a uniform frame2 work. Typically, there is some natural transformation from satis ability for the standard modal logics B, S4, S5 into PDL with converse (see e.g. ....
....ability into converse CPDL satis ability. Proof Roughly speaking, the modal connectives [c m 1 ] and [c m 1 ] behave independently of the modal connectives involving exclusively the program constants c 1 ; cm . By [Spa93] converse CPDL is EXPTIME hard. converse CPDL is in EXPTIME [Gia95, ABM00] (see also [PT91] Let us de ne a logarithmic space transformation f satis ability into converse CPDL satis ability. f is de ned as f from L m into PDL except that the point 1. is replaced by: for any atomic formula p (either propositional variable or nominal) f(p) p. ....
G. de Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita Degli Studi Di Roma 'La Sapienza', 1995. Available via http://www.dis.uniroma1.it/degiacom/publications.html on WWW.
Path Constraints from a Modal Logic Point of View (Extended.. - Alechina, al. (2001) (Correct)
....web. We have obtained sharp upper and lower bounds that are better than previously known ones (Theorems 11 and 12) Table 1 summarizes the complexity and (un ) decidability results for the logics considered in this paper. Some of our decidability results were obtained by re using the results of [12]. In fact, there are many areas in computer science in which describing and reasoning about nite graphs is a key issue. There exists a large body of work in e.g. feature structures [23] process algebra [19] or knowledge representation [13] which can be usefully applied in database theory. But ....
.... 8 paper, Theorem 8 Satis ability problem non deterministic graphs deterministic graphs PDL EXPTIME complete [14, 22] EXPTIME complete [20, 5] PDL with nominals EXPTIME complete [15] EXPTIME complete [15] CPDL EXPTIME complete [14, 22] EXPTIME complete [25] CPDL with nominals EXPTIME complete [12, 4] open PDL path EXPTIME complete; this open paper, Theorem 10 Implication problem non deterministic graphs deterministic graphs inclusion constraints PSPACE hard, in EXPTIME; open this paper, Theorem 11 backward constraints PSPACE hard, in EXPTIME; in EXPTIME (with nite L) this paper, ....
G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita degli Studi di Roma \La Sapienza", 1995.
Decidable Fragments of First-Order Modal Logics - Wolter, Zakharyaschev (1999) (4 citations) (Correct)
.... non modal part of ALCM is in principle nothing else but the polymodal propositional logic K (this fact was rst observed in [33] There are, however, much more expressive (and yet decidable) concept description languages; see e.g. 8] Here is only one example, the logic CI introduced in [15, 16]. Its syntax allows the formation of the union R S of roles R and S, their composition R S, the re exive and transitive closure R , and the inversion R of R; moreover, every concept C gives rise to the role C (the set of all pairs hx; xi such that x 2 C) This language may be regarded as ....
....of which are structures from FO, is decidable. 22 FRANK WOLTER AND MICHAEL ZAKHARYASCHEV Corollary 6.6. The satis ability problem for the modal description logic CIM (the modal operators 2 i are applied to both concepts and formulas) is decidable. Proof. That (i) holds was actually shown in [15], and (ii) follows from the fact that the class of rst order structures for CI is closed under the disjoint unions. a For more decidability results of this sort see [49, 46, 50, 47] As was observed in [12] the one variable fragment of a rst order modal logic can be regarded as the Cartesian ....
G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Univ. di Roma, 1995.
Path Constraints from a Modal Logic Point of View.. - Alechina, Demri, de.. (Correct)
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G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita degli Studi di Roma \La Sapienza", 1995.
Relativized Action Complement for Dynamic Logics - Broersen (Correct)
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G. De Giacomo. Decidability of class-based knowledge representation formalisms. PhD thesis, Universita' di Roma \La Sapienza", 1995.
A Description Logic Model for Reacting in a Dynamic.. - Kullmann, de Beuvron.. (Correct)
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G. de Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita di Roma \La Sapienza", Italy, 1995.
Path Constraints from a Modal Logic Point of View.. - Alechina, Demri, de.. (Correct)
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G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita degli Studi di Roma \La Sapienza", 1995.
Mary Likes all Cats - Lutz, Sattler (2000) (Correct)
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G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita degli Studi di Roma \La Sapienza", 1995.
Basic Description Logics - Baader, Nutt (2003) (14 citations) (Correct)
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Giuseppe De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Dipartimento di Informatica e Sistemistica, Universita di Roma \La Sapienza", 1995.
Logic Programming: The Case of Description and Hybrid Logic - Areces (Correct)
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G. De Giacomo. Decidability of Class-based Knowledge Representation Formalisms. PhD thesis, Universita di Roma \La Sapienza", 1995.
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