Donini, F. M.; Nardi, D.; and Rosati, R. 1997. Ground nonmonotonic modal logics. Journal of Logic and Computation 7(4):523--548.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... e.g. in (Halpern Moses 1985) However, the bestknown such reconstruction is (Levesque 1990) extended and discussed in (Halpern Lakemeyer 1995) Lakemeyer 1993; 1996) and (Lakemeyer Levesque 1998) For an overview of the relationships between these closely related approaches, see (Donini, Nardi, Rosati 1997) and (Rosati 2000) Chen (1997) presents an analysis relating Levesque s concept of only knowing to the method of epistemic specifications of (Gelfond 1991) # The author thanks Nick Player, Manfred Jaeger and Renate Schmidt for their comments on earlier drafts of this paper. Copyright c # ....

Donini, F. M.; Nardi, D.; and Rosati, R. 1997. Ground nonmonotonic modal logics. Journal of Logic and Computation 7(4):523--548.

....reasoning, originally proposed by Halpern and Moses (1985) Their aim was to formalize statements of the form I only know . It allows, for example, to derive that an agent which only knows p, does not know q. Ground S5 falls into the general scheme of ground nonmonotonic modal logics (Donini, Nardi, Rosati, 1997). A lot of interest is devoted to logics of minimal knowledge (Levesque, 1990; Schwarz Truszczy nski, 1994; Chen, 1997; Halpern, 1997) Semantically, states in which an agent only knows , are states in which is known, but otherwise the amount of knowledge is minimal. We will use a modal ....

....is smooth, so the conservative formulae are exactly the upward persistent formulae, which express only knowledge (and not ignorance) This can be lifted again to an infinite language. The fact that in Ground S5, formulae that express propositional knowledge, are conservative, was already noted by Donini et al. 1997). MTEL also satisfies expressibility of preference (for a finite language) so any formula that is conservative, must be upward persistent, and must be equivalent to a formula in TB, expressing knowledge over time (not ignorance) This can be lifted to an infinite language. Unfortunately, MTEL is ....

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Donini, F. M., Nardi, D., & Rosati, R. (1997). Ground nonmonotonic modal logics. Journal of Logic and Computation, 7 (4), 523--548.

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Donini, F. M.; Nardi, D.; and Rosati, R. 1997. Ground nonmonotonic modal logics. J. of Logic and Computation 7(4):523--548.

....is harder than for the above presented nonmonotonic logics. In particular, it is a p 2 complete problem. However, logical inference in such logics 98 of minimal knowledge is harder than in default logic and autoepistemic logic, since it is a p 3 complete problem both in MKNF and in S5G [4, 16]. Hence, also in such formalisms model checking is easier than logical inference. We rst analyze modal logic S5G , i.e. the logic of minimal knowledge introduced in [7] Theorem 8. Let 2 LK , f 2 L. Then, the problem of establishing whether M = fI : I j= fg is an S5G model of is p 2 ....

F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics. J. of Log. and Comp., 7(4):523-548, Aug. 1997.

.... shown in [16] Sigma corresponds to the default theory (f bird : flies flies g; bird) It turns out that, when restricting to theories composed of K formulas, MKNF corresponds to the modal logic of minimal knowledge due to Halpern and Moses [9] also known as ground nonmonotonic modal logic S5G [11,4]. Moreover, it has been shown [18,22] that, under the restriction that the theory be composed of A formulas, MKNF corresponds to Moore s autoepistemic logic [20] Consequently, the logic MKNF can be interpreted as a generalization of both Halpern and Moses logic of minimal knowledge and Moore s ....

F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics. J. of Logic and Computation, 7(4):523--548, Aug. 1997.

....than for the above presented nonmonotonic logics. In particular, it is a Sigma p 2 complete problem. However, logical inference in such logics of minimal knowledge is harder than in default logic and autoepistemic logic, since it is a Pi p 3 complete problem both in MKNF and in S5G [ Donini et al. 1997; Rosati, 1997 ] Hence, also in such formalisms model checking is easier than logical inference. We first analyze modal logic S5G , i.e. the logic of minimal knowledge introduced in [ Halpern and Moses, 1985 ] Theorem 12 Let Sigma 2 LK , f 2 L. Then, the problem of establishing whether M = ....

F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics. J. of Logic and Computation, 7(4):523--548, 1997.

.... minimal knowledge operator K and a negation as failure (or negation by default ) operator not . In particular, the modality K coincides with the epistemic operator of the modal logic defined by Halpern and Moses in [ Halpern Moses, 1985 ] also known as ground nonmonotonic modal logic S5G [ Donini, Nardi, Rosati, 1997b ] which modifies modal logic S5 through a very intuitive preference semantics [ Shoham, 1987 ] consider only the models of the knowledge base (i.e. the epistemic states of the agent modeled) in which the knowledge on the objective facts is minimal (i.e. the ignorance of the agent is ....

....as failure. For this reason it is also considered a very expressive formalism. Recently, MKNF has also been regarded as a suitable knowledge representation formalism, since the combined usage of its modalities allows for the formalization of several nonmonotonic features of frame based systems [ Donini, Nardi, Rosati, 1997b ] As a consequence, the computational properties of MKNF have been investigated. It has been proven [ Rosati, 1997 ] that reasoning in propositional MKNF is harder than reasoning in all the best known propositional nonmonotonic logics. In particular, it has been shown that such an higher ....

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F. M. Donini, D. Nardi, and R. Rosati, 1997. Ground nonmonotonic modal logics. Journal of Logic and Computation, 7(4). To appear.

.... interest in defining deductive methods for MBNF also arises from the fact that such a logic, originally developed as a framework for the comparison of different logical approaches to nonmonotonic reasoning, has recently been considered as an attractive knowledge representation formalism (see e.g. (Donini, Nardi, Rosati 1997b) In this paper we present a computational characterization and provide optimal algorithms for deduction in the propositional fragment of MBNF . In particular, we show that skeptical reasoning in the propositional fragment of MBNF is a Pi p 3 complete problem: hence, it is harder (unless ....

....0 ) where Sigma 0 = Sigma :not(P ) a) P 0 ; N 0 ) is not consistent with Sigma 0 or (b) P 6 P 0 or (c) P 0 P or (d) P 6 N 0 then return true else return false end Figure 2: Algorithm MBNF Not Entails. as ground nonmonotonic modal logic S5G (Donini, Nardi, Rosati 1997). Indeed, it is easy to see that, for positive subjective MBNF theories, there is a one to one correspondence between MBNF models of a theory Sigma and S5G models of the theory Sigma K . Proposition 13 Let Sigma 2 L S M . Then, I ; M) is an MBNF model for Sigma iff M is an S5G model ....

[Article contains additional citation context not shown here]

F. M. Donini, D. Nardi, and R. Rosati, 1997. Ground nonmonotonic modal logics. Journal of Logic and Computation, 7(4). To appear.

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Donini, F. M.; Nardi, D.; and Rosati, R. 1997. Ground nonmonotonic modal logics. Journal of Logic and Computation 7(4):523--548.

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