356 research outputs found
Algebra and Sequent Calculus for Epistemic Actions
We introduce an algebraic approach to Dynamic Epistemic Logic. This approach has the advantage that: (i) its semantics is a transparent algebraic object with a minimal set of primitives from which most ingredients of Dynamic Epistemic Logic arise, (ii) it goes with the introduction of non-determinism, (iii) it naturally extends beyond boolean sets of propositions, up to intuitionistic and non-distributive situations, hence allowing to accommodate constructive computational, information-theoretic as well as non-classical physical settings, and (iv) introduces a structure on the actions, which now constitute a quantale. We also introduce a corresponding sequent calculus (which extends Lambek calculus), in which propositions, actions as well as agents appear as resources in a resource-sensitive dynamic-epistemic logic
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
Tool support for reasoning in display calculi
We present a tool for reasoning in and about propositional sequent calculi.
One aim is to support reasoning in calculi that contain a hundred rules or
more, so that even relatively small pen and paper derivations become tedious
and error prone. As an example, we implement the display calculus D.EAK of
dynamic epistemic logic. Second, we provide embeddings of the calculus in the
theorem prover Isabelle for formalising proofs about D.EAK. As a case study we
show that the solution of the muddy children puzzle is derivable for any number
of muddy children. Third, there is a set of meta-tools, that allows us to adapt
the tool for a wide variety of user defined calculi
A Spatial-Epistemic Logic for Reasoning about Security Protocols
Reasoning about security properties involves reasoning about where the
information of a system is located, and how it evolves over time. While most
security analysis techniques need to cope with some notions of information
locality and knowledge propagation, usually they do not provide a general
language for expressing arbitrary properties involving local knowledge and
knowledge transfer. Building on this observation, we introduce a framework for
security protocol analysis based on dynamic spatial logic specifications. Our
computational model is a variant of existing pi-calculi, while specifications
are expressed in a dynamic spatial logic extended with an epistemic operator.
We present the syntax and semantics of the model and logic, and discuss the
expressiveness of the approach, showing it complete for passive attackers. We
also prove that generic Dolev-Yao attackers may be mechanically determined for
any deterministic finite protocol, and discuss how this result may be used to
reason about security properties of open systems. We also present a
model-checking algorithm for our logic, which has been implemented as an
extension to the SLMC system.Comment: In Proceedings SecCo 2010, arXiv:1102.516
Reasoning about Knowledge in Linear Logic: Modalities and Complexity
In a recent paper, Jean-Yves Girard commented that âit has been a long time since philosophy has stopped intereacting with logicâ[17]. Actually, it has no
Dynamic Sequent Calculus for the Logic of Epistemic Actions and Knowledge
Dynamic Logics (DLs) form a large family of nonclassical logics, and perhaps the one enjoying the widest range of applications. Indeed, they are designed to formalize change caused by actions of diverse nature: updates on the memory state of a computer, displacements of moving robots in an environment, measurements in models of quantum physics, belief revisions, knowledge updates, etc. In each of these areas, DL-formulas express properties of the model encoding the present state of affairs, as well as the pre- and post-conditions of a given action. Actions are semantically represented as transformations of one model into another, encoding the state of affairs after the action has taken place. DL-languages are expansions of classical (static) logic with dynamic operators, parametrized with actions; dynamic operators are modalities interpreted in terms of the transformation of models corresponding to their action-parameters
Aximo: automated axiomatic reasoning for information update
Aximo is a software written in C++ that verifies epistemic properties of dynamic scenarios in multi-agent systems. The underlying logic of our tool is based on the algebraic axiomatics of Dynamic Epistemic Logic. We also present a new theoretical result: the worst case complexity of the verification problem of Aximo
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