WOOLDRIDGE, M., DIXON, C., AND FISHER, M. 1998. A tableau-based proof method for temporal logics of knowledge and belief. J. Appl. Non-Classical Logics 8 (1988), 225--258.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....by Fitting [6] Gor e [10] Massacci [14] and ours [15] As some recent works devoted to developing tableau systems for modal logics about knowledge or belief, there are the works by Fitting et The axioms I and C are named by us. al [7] Rosati [17] Baldoni et al. [2] and Wooldridge et al. [20]. Besides, tableau algorithms have been also developed for description logics, which are a family of knowledge representation formalisms (see the overview by Baader and Sattler [1] The mentioned works [7, 17, 2, 20] however, do not suit to reasoning about both knowledge and belief: the ....

....I and C are named by us. al [7] Rosati [17] Baldoni et al. [2] and Wooldridge et al. [20] Besides, tableau algorithms have been also developed for description logics, which are a family of knowledge representation formalisms (see the overview by Baader and Sattler [1] The mentioned works [7, 17, 2, 20], however, do not suit to reasoning about both knowledge and belief: the multimodal logics studied in [7, 20] have modalities of the same type, the grammar logics considered in [2] have modalities of di erent types but do not contain the axioms D and 5. In this paper, basing on known tableau ....

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M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225-258, 1998. 15

....we are investigating an approach with the following properties: The approach covers the combination of discrete, linear, temporal logic with extensions of multi modal Km by any combination of the axiom schemata 4, 5, B, D, and T. This extends the results presented in (Dixon, Fisher and Wooldridge 1998; Wooldridge, Dixon, and Fisher 1998) Instead of combining two calculi operating according to the same underlying principles, like for example two tableaux based calculi, we combine two different approaches to theorem proving in modal and temporal logics, namely the translation approach for ....

....an approach with the following properties: The approach covers the combination of discrete, linear, temporal logic with extensions of multi modal Km by any combination of the axiom schemata 4, 5, B, D, and T. This extends the results presented in (Dixon, Fisher and Wooldridge 1998; Wooldridge, Dixon, and Fisher 1998). Instead of combining two calculi operating according to the same underlying principles, like for example two tableaux based calculi, we combine two different approaches to theorem proving in modal and temporal logics, namely the translation approach for modal logics (using first order ....

Wooldridge, M., Dixon, C., and Fisher, M. (1998). A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225--258.

....enough to describe the static aspect of the world. In particular, there is a need to formalize its temporal evolution as well. Consequently, over the last years we have observed a growing interest in so called temporalizations of logical formalisms. We mention [14, 15] for a general approach, [13, 34] for extensions of epistemic logics by means of temporal operators to model, among others, multi agent systems, 33] which supplies a logic of space with temporal operators in order to describe the evolution of regions in time, 1, 12] for work on temporal databases, and [20, 23, 24, 28] which ....

....has been made as concerns the determination of the decidability and complexity of temporalized systems, witness [19, 24, 25, 32] on the other hand, only very few implementable algorithms i.e. tableaux or resolution algorithms have been suggested. Laudable exceptions are the work of [2, 5, 25, 34]. In this paper we follow the latter line of research and develop a tableau algorithm for the extension of ALC introduced in [32] interpreted, however, not in models with constant domain but in models with increasing domains. 2 That is to say, we extend the language of ALC by means of the ....

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M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-classical Logics, 8:225 -- 258, 1998.

No context found.

M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

No context found.

M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

.... a variety of interactions are considered [6, 12, 14, 15] Resolution based proof methods for the single agent cases of synchrony and perfect recall are given in [2] and for synchrony and no learning [19] A tableau based proof method for the fusion of PTL plus either S5 or KD45 is given in [28]. This is essentially the combination of tableau methods for propositional linear time temporal logics [27] and that for the modal logics S5 and KD45 [11] It does not require the translation to any particular normal form. The work on proof methods for BDI logics given in [21, 22] give a tableau ....

M. Wooldridge, C. Dixon, and M. Fisher. A TableauBased Proof Method for Temporal Logics of Knowledge and Belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

....to achieve. Planning is then viewed as a process of checking that the formula representing the goal is satisfied in the model representing the domain. Most work in this area has used Computation Tree Logic (CTL) 8] In our approach, we use a temporal logic that incorporates knowledge operators [19]. This logic is called Alternating Temporal Epistemic Logic (ATEL) and is an extension of the Alternating Temporal Logic (ATL) of Alur, Henzinger, and Kupferman [3] ATL is a novel generalisation of CTL in which the path quantifiers of CTL are replaced by cooperation modalities: the ATL formula ....

M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

.... deployed in the formal speci cation of distributed systems, where they are used to make precise the concept of what a process knows [6, 18] Temporal logics of knowledge temporal logics enriched by modal knowledge operators have also been widely used for reasoning about distributed systems [9, 25]. Model checking as an approach to the automatic veri cation of nite state systems has focussed predominantly on system speci cations expressed in temporal logic linear temporal logic in the case of spin [13, 14] and forspec [24] branching temporal logic in the case of smv [17] and its ....

M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225-258, 1998.

....logics are used to capture the detailed behaviour of the application domain. While many of the basic properties of such combinations are well understood (Baader and Ohlbach 1995; Fagin et al. 1996; Gabbay 1996; Wolter 1998) very little work has been carried out on proof methods for such logics. Wooldridge, Dixon, and Fisher (1998) present a tableaux based calculus for the combination of discrete linear temporal logic with the modal logics KD45 (characterising belief) and S5 (characterising knowledge) Dixon, Fisher, and Wooldridge (1998) present a resolution based calculus for the combination of discrete linear temporal ....

....little work has been carried out on proof methods for such logics. Wooldridge, Dixon, and Fisher (1998) present a tableaux based calculus for the combination of discrete linear temporal logic with the modal logics KD45 (characterising belief) and S5 (characterising knowledge) Dixon, Fisher, and Wooldridge (1998) present a resolution based calculus for the combination of discrete linear temporal logic with the modal logic S5. A combination of calendar logic for specifying everyday temporal notions with a variety of other modal logics has been considered in (Ohlbach 1998; Ohlbach and Gabbay 1998) Our aim ....

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Wooldridge, M., Dixon, C., and Fisher, M. (1998). A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225--258.

....of the algorithms facilitates optimised implementation. ai rev00.tex; 13 07 2000; 13:21; p. 6 7 We have developed a range of tableaux based systems for description logics, for example (Horrocks, 1998a; Horrocks, 2000) and for combinations of linear time temporal logic with modal logics S5 or KD45 (Wooldridge et al. 1998). 4.2. RESOLUTION BASED REASONING An alternative approach to reasoning in combined modal logics is to use direct resolution techniques which should, in the long term have at least the performance of corresponding tableaux based systems. Our work in this area has focused on extending the ....

M. Wooldridge, C. Dixon, and M. Fisher. A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

....for combined logics. A resolution based method for linear time temporal logic with finite past and infinite future (PTL) plus a single copy of the modal logic S5 is given in [6] A tableau algorithm for the multi modal version of this logic and PTL combined with multi modal KD45 is presented in [25]. Tableau based proof methods for Belief Desire Intention (BDI) Logics (combining linear or branching time temporal logics with the modal logics KD45 and KD) can be found in [20, 22] Halpern, Vardi et al. provide complete axiomatisations for temporal logics of knowledge in [10] and consider ....

....temporal logics (CTL and CTL ) with the modal logics with the modal logics KD45 for belief and KD for desire and intention. In [22] interactions between the modal components are also considered. Tableau methods for PTL combined with multi modal S5 or multi modal KD45 are also considered in [25]. Tableaux methods for description logics (essentially combinations of modal logics) have been described and implemented in [12] Halpern, Vardi et al. consider the combination of propositional linear and branching time temporal logics with multi modal S5 allowing a variety of interactions in ....

M. Wooldridge, C. Dixon, and M. Fisher. A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

....to agent j) Temporal extensions. The emphasis in this work has been on classifying instananeous relationships in VSK logic. Much work remains to be done in considering the temporal extensions to the logic, in much the same way that epistemic logic is extended into the temporal dimension in [15]. Knowledge based programs. The relationship between VSK logic and knowledge based programs [5, Chapter 7] would also be an interesting area of future work: VSK logic has something to say about when such programs are implementable. ....

M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

No context found.

WOOLDRIDGE, M., DIXON, C., AND FISHER, M. 1998. A tableau-based proof method for temporal logics of knowledge and belief. J. Appl. Non-Classical Logics 8 (1988), 225--258.

No context found.

Wooldridge, M., C. Dixon and M. Fisher, A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief, Journal of Applied Non-Classical Logics 8 (1998), pp. 225-258. 15

No context found.

Wooldridge, M., C. Dixon, and M. Fisher, `A tableau-based proof method for temporal logics of knowledge and belief', Journal of Applied Non-Classical Logics, 8(3):225--258, 1998.

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M. Wooldridge, C. Dixon, M. Fisher, "A tableau-based proof method for temporal logics of knowledge and belief", Journal of Applied Non-Classical Logics, vol. 6 (3), pp. 225--258, 1998.

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Wooldridge, M., C. Dixon and M. Fisher, A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief, Journal of Applied Non-Classical Logics 8 (1998), pp. 225-258. 15

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M. Wooldridge, C. Dixon, and M. Fisher. A tableau-based proof method for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics, 8(3), 1998.

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