1,697 research outputs found
Set-Theoretic Completeness for Epistemic and Conditional Logic
The standard approach to logic in the literature in philosophy and
mathematics, which has also been adopted in computer science, is to define a
language (the syntax), an appropriate class of models together with an
interpretation of formulas in the language (the semantics), a collection of
axioms and rules of inference characterizing reasoning (the proof theory), and
then relate the proof theory to the semantics via soundness and completeness
results. Here we consider an approach that is more common in the economics
literature, which works purely at the semantic, set-theoretic level. We provide
set-theoretic completeness results for a number of epistemic and conditional
logics, and contrast the expressive power of the syntactic and set-theoretic
approachesComment: This is an expanded version of a paper that appeared in AI and
Mathematics, 199
The Power of Proofs: New Algorithms for Timed Automata Model Checking (with Appendix)
This paper presents the first model-checking algorithm for an expressive
modal mu-calculus over timed automata, , and reports performance results for an implementation.
This mu-calculus contains extended time-modality operators and can express all
of TCTL. Our algorithmic approach uses an "on-the-fly" strategy based on proof
search as a means of ensuring high performance for both positive and negative
answers to model-checking questions. In particular, a set of proof rules for
solving model-checking problems are given and proved sound and complete; we
encode our algorithm in these proof rules and model-check a property by
constructing a proof (or showing none exists) using these rules. One noteworthy
aspect of our technique is that we show that verification performance can be
improved with \emph{derived rules}, whose correctness can be inferred from the
more primitive rules on which they are based. In this paper, we give the basic
proof rules underlying our method, describe derived proof rules to improve
performance, and compare our implementation of this model checker to the UPPAAL
tool.Comment: This is the preprint of the FORMATS 2014 paper, but this is the full
version, containing the Appendix. The final publication is published from
Springer, and is available at
http://link.springer.com/chapter/10.1007%2F978-3-319-10512-3_9 on the
Springer webpag
Sequent Calculus in the Topos of Trees
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic,
has been applied in type systems and program logics to capture guarded
recursion. Birkedal et al modelled this modality via the internal logic of the
topos of trees. We show that the semantics of the propositional fragment of
this logic can be given by linear converse-well-founded intuitionistic Kripke
frames, so this logic is a marriage of the intuitionistic modal logic KM and
the intermediate logic LC. We therefore call this logic
. We give a sound and cut-free complete sequent
calculus for via a strategy that decomposes
implication into its static and irreflexive components. Our calculus provides
deterministic and terminating backward proof-search, yields decidability of the
logic and the coNP-completeness of its validity problem. Our calculus and
decision procedure can be restricted to drop linearity and hence capture KM.Comment: Extended version, with full proof details, of a paper accepted to
FoSSaCS 2015 (this version edited to fix some minor typos
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
Positive Logic with Adjoint Modalities: Proof Theory, Semantics and Reasoning about Information
We consider a simple modal logic whose non-modal part has conjunction and
disjunction as connectives and whose modalities come in adjoint pairs, but are
not in general closure operators. Despite absence of negation and implication,
and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and
S5, such logics are useful, as shown in previous work by Baltag, Coecke and the
first author, for encoding and reasoning about information and misinformation
in multi-agent systems. For such a logic we present an algebraic semantics,
using lattices with agent-indexed families of adjoint pairs of operators, and a
cut-free sequent calculus. The calculus exploits operators on sequents, in the
style of "nested" or "tree-sequent" calculi; cut-admissibility is shown by
constructive syntactic methods. The applicability of the logic is illustrated
by reasoning about the muddy children puzzle, for which the calculus is
augmented with extra rules to express the facts of the muddy children scenario.Comment: This paper is the full version of the article that is to appear in
the ENTCS proceedings of the 25th conference on the Mathematical Foundations
of Programming Semantics (MFPS), April 2009, University of Oxfor
Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General
This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment
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+
Evidence and plausibility in neighborhood structures
The intuitive notion of evidence has both semantic and syntactic features. In
this paper, we develop an {\em evidence logic} for epistemic agents faced with
possibly contradictory evidence from different sources. The logic is based on a
neighborhood semantics, where a neighborhood indicates that the agent has
reason to believe that the true state of the world lies in . Further notions
of relative plausibility between worlds and beliefs based on the latter
ordering are then defined in terms of this evidence structure, yielding our
intended models for evidence-based beliefs. In addition, we also consider a
second more general flavor, where belief and plausibility are modeled using
additional primitive relations, and we prove a representation theorem showing
that each such general model is a -morphic image of an intended one. This
semantics invites a number of natural special cases, depending on how uniform
we make the evidence sets, and how coherent their total structure. We give a
structural study of the resulting `uniform' and `flat' models. Our main result
are sound and complete axiomatizations for the logics of all four major model
classes with respect to the modal language of evidence, belief and safe belief.
We conclude with an outlook toward logics for the dynamics of changing
evidence, and the resulting language extensions and connections with logics of
plausibility change
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