27,701 research outputs found
Axiomatization of the AGM theory of belief revision in a temporal logic
It is natural to think of belief revision as the interaction of belief
and information over time. Thus branching-time temporal logic seems a natural
setting for a theory of belief revision. We propose two extensions of a
modal logic that, besides the ""next-time"" temporal operator, contains a
belief operator and an information operator. The first logic is shown to
provide an axiomatization of the first six postulates of the AGM theory
of belief revision, while the second, stronger, logic provides an axiomatization
of the full set of AGM postulates.Belief revision, information, temporal logic, AGM theory
Satisfiability Games for Branching-Time Logics
The satisfiability problem for branching-time temporal logics like CTL*, CTL
and CTL+ has important applications in program specification and verification.
Their computational complexities are known: CTL* and CTL+ are complete for
doubly exponential time, CTL is complete for single exponential time. Some
decision procedures for these logics are known; they use tree automata,
tableaux or axiom systems. In this paper we present a uniform game-theoretic
framework for the satisfiability problem of these branching-time temporal
logics. We define satisfiability games for the full branching-time temporal
logic CTL* using a high-level definition of winning condition that captures the
essence of well-foundedness of least fixpoint unfoldings. These winning
conditions form formal languages of \omega-words. We analyse which kinds of
deterministic {\omega}-automata are needed in which case in order to recognise
these languages. We then obtain a reduction to the problem of solving parity or
B\"uchi games. The worst-case complexity of the obtained algorithms matches the
known lower bounds for these logics. This approach provides a uniform, yet
complexity-theoretically optimal treatment of satisfiability for branching-time
temporal logics. It separates the use of temporal logic machinery from the use
of automata thus preserving a syntactical relationship between the input
formula and the object that represents satisfiability, i.e. a winning strategy
in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner
closure of the input formula only. Last but not least, the games presented here
come with an attempt at providing tool support for the satisfiability problem
of complex branching-time logics like CTL* and CTL+
BRANCHING TIME LOGIC, PERFECT INFORMATION GAMES AND BACKWARD INDUCTION
The logical foundations of game-theoretic solution concepts have so far been developed within the confines of epistemic logic. In this paper we turn to a different branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. We extend the branching time framework by adding agents and by defining the notion of prediction. We show that perfect information games are a special case of extended branching time frames and that the backward-induction solution is a prediction. We also provide a characterization of backward induction in terms of the property of internal consistency of prediction.
A clausal resolution for extended computation tree logic ECTL
A temporal clausal resolution method was originally
developed for linear time temporal logic and further extended to the branching-time framework of Computation Tree Logic (CTL). In this paper, following our general idea
to expand the applicability of this efficient method to more
expressive formalisms useful in a variety of applications
in computer science and AI requiring branching time logics,
we define a clausal resolution technique for Extended
Computation Tree Logic (ECTL). The branching-time temporal
logic ECTL is strictly more expressive than CTL, in
allowing fairness operators. The key elements of the resolution method for ECTL, namely the clausal normal form, the concepts of step resolution and a temporal resolution,
are introduced and justified with respect to this new framework.
Although in developing these components we incorporate
many of the techniques defined for CTL, we need novel mechanisms in order to capture fairness together with the limit closure property of the underlying tree models.
We accompany our presentation of the relevant techniques
by examples of the application of the temporal resolution
method. Finally, we provide a correctness argument and
consider future work discussing an extension of the method
yet further, to the logic CTL*, the most powerful logic of
this class
Belief change in branching time: AGM-consistency and iterated revision
We study belief change branching-time structures. First, we identify a property of branching-time frames that is equivalent to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in [Bonanno, Axiomatic characterization of the AGM theory of belief revision in a temporal logic, Artificial Intelligence, 2007]. Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.iterated belief revision, branching time, information, belief, modal logic, AGM belief revision
Automating natural deduction for temporal logic
We present our recent work on the construction of natural deduction calculi for temporal logic. We analyse propositional linear-time temporal logic (PLTL) and Computation Tree Logic (CTL) and corresponding proof searching algorithms.
The automation of the natural deduction calculi for these temporal logics opens the new prospect to apply our
techniques as an automatic reasoning tool in the areas, where the linear-time or branching-time setting is required
Logic and model checking for hidden Markov models
The branching-time temporal logic PCTL* has been introduced to specify quantitative properties over probability systems, such as discrete-time Markov chains. Until now, however, no logics have been defined to specify properties over hidden Markov models (HMMs). In HMMs the states are hidden, and the hidden processes produce a sequence of observations. In this paper we extend the logic PCTL* to POCTL*. With our logic one can state properties such as "there is at least a 90 percent probability that the model produces a given sequence of observations" over HMMs. Subsequently, we give model checking algorithms for POCTL* over HMMs
Natural deduction calculus for computation tree logic
The authors present a natural deduction calculus for the computation tree logic, CTL, defined with the full set of classical and temporal logic operators. The system extends the natural deduction construction of the linear-time temporal logic. This opens the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various applications in AI and computer science, where the branching-time setting is required
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