52 research outputs found
To Be Announced
In this survey we review dynamic epistemic logics with modalities for
quantification over information change. Of such logics we present complete
axiomatizations, focussing on axioms involving the interaction between
knowledge and such quantifiers, we report on their relative expressivity, on
decidability and on the complexity of model checking and satisfiability, and on
applications. We focus on open problems and new directions for research
The Modal Logic of Stepwise Removal
We investigate the modal logic of stepwise removal of objects, both for its
intrinsic interest as a logic of quantification without replacement, and as a
pilot study to better understand the complexity jumps between dynamic epistemic
logics of model transformations and logics of freely chosen graph changes that
get registered in a growing memory. After introducing this logic
() and its corresponding removal modality, we analyze its
expressive power and prove a bisimulation characterization theorem. We then
provide a complete Hilbert-style axiomatization for the logic of stepwise
removal in a hybrid language enriched with nominals and public announcement
operators. Next, we show that model-checking for is
PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we
consider an issue of fine-structure: the expressive power gained by adding the
stepwise removal modality to fragments of first-order logic
Refinement Modal Logic
In this paper we present {\em refinement modal logic}. A refinement is like a
bisimulation, except that from the three relational requirements only `atoms'
and `back' need to be satisfied. Our logic contains a new operator 'all' in
addition to the standard modalities 'box' for each agent. The operator 'all'
acts as a quantifier over the set of all refinements of a given model. As a
variation on a bisimulation quantifier, this refinement operator or refinement
quantifier 'all' can be seen as quantifying over a variable not occurring in
the formula bound by it. The logic combines the simplicity of multi-agent modal
logic with some powers of monadic second-order quantification. We present a
sound and complete axiomatization of multi-agent refinement modal logic. We
also present an extension of the logic to the modal mu-calculus, and an
axiomatization for the single-agent version of this logic. Examples and
applications are also discussed: to software verification and design (the set
of agents can also be seen as a set of actions), and to dynamic epistemic
logic. We further give detailed results on the complexity of satisfiability,
and on succinctness
Undecidability in Epistemic Planning
Dynamic epistemic logic (DEL) provides a very expressive framework for multi-agent planning that can deal with nondeterminism, partial observability, sensing actions, and arbitrary nesting of beliefs about other agents’ beliefs. However, as we show in this paper, this expressiveness comes at a price. The planning framework is undecidable, even if we allow only purely epistemic actions (actions that change only beliefs, not ontic facts). Undecidability holds already in the S5 setting with at least 2 agents, and even with 1 agent in S4. It shows that multi-agent planning is robustly undecidable if we assume that agents can reason with an arbitrary nesting of beliefs about beliefs. We also prove a corollary showing undecidability of the DEL model checking problem with the star operator on actions (iteration)
Satisfiability of Arbitrary Public Announcement Logic with Common Knowledge is -hard
Arbitrary Public Announcement Logic with Common Knowledge (APALC) is an
extension of Public Announcement Logic with common knowledge modality and
quantifiers over announcements. We show that the satisfiability problem of
APALC on S5-models, as well as that of two other related logics with
quantification and common knowledge, is -hard. This implies that
neither the validities nor the satisfiable formulas of APALC are recursively
enumerable. Which, in turn, implies that APALC is not finitely axiomatisable.Comment: In Proceedings TARK 2023, arXiv:2307.0400
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Logic, Rational Agency, and Intelligent Interaction
... make a plea for recasting logic as a theory of interactive agency, and show how this perspective fits both old achievements and new broader ambitions for the field
Dynamic epistemic verification of security protocols: framework and case study
We propose a dynamic epistemic framework for the verification of security protocols. First, we introduce a dynamic epistemic logic equipped with iteration and cryptographic supplements in which we can formalize and check (epistemic) requirements of security protocols. On top of this, we give a general guide how to go from a protocol specification to its representation in our framework. We demonstrate this by checking requirements of a simplified version of a protocol for confidential message comparison
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