9,336 research outputs found
Agency and fictional truth: a formal study on fiction-making
Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language L of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of L with respect to other modal languages is a variety of operators having to do with fictional truth, including a \u2018fictionality\u2019 operator M (to be read as \u201cit is a fictional truth that\u201d). Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for
A Faster Tableau for CTL*
There have been several recent suggestions for tableau systems for deciding
satisfiability in the practically important branching time temporal logic known
as CTL*. In this paper we present a streamlined and more traditional tableau
approach built upon the author's earlier theoretical work.
Soundness and completeness results are proved. A prototype implementation
demonstrates the significantly improved performance of the new approach on a
range of test formulas. We also see that it compares favourably to state of the
art, game and automata based decision procedures.Comment: In Proceedings GandALF 2013, arXiv:1307.416
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+
Cut-free Calculi and Relational Semantics for Temporal STIT Logics
We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames
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