4,000 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
Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism
This essay examines the philosophical significance of -logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of -logical validity can then be countenanced within a coalgebraic logic, and -logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of -logical validity correspond to those of second-order logical consequence, -logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets
Modeling of Phenomena and Dynamic Logic of Phenomena
Modeling of complex phenomena such as the mind presents tremendous
computational complexity challenges. Modeling field theory (MFT) addresses
these challenges in a non-traditional way. The main idea behind MFT is to match
levels of uncertainty of the model (also, problem or theory) with levels of
uncertainty of the evaluation criterion used to identify that model. When a
model becomes more certain, then the evaluation criterion is adjusted
dynamically to match that change to the model. This process is called the
Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes
of the mind and natural evolution. This paper provides a formal description of
DLP by specifying its syntax, semantics, and reasoning system. We also outline
links between DLP and other logical approaches. Computational complexity issues
that motivate this work are presented using an example of polynomial models
Categories for Dynamic Epistemic Logic
The primary goal of this paper is to recast the semantics of modal logic, and
dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We
first review the category of relations and categories of Kripke frames, with
particular emphasis on the duality between relations and adjoint homomorphisms.
Using these categories, we then reformulate the semantics of DEL in a more
categorical and algebraic form. Several virtues of the new formulation will be
demonstrated: The DEL idea of updating a model into another is captured
naturally by the categorical perspective -- which emphasizes a family of
objects and structural relationships among them, as opposed to a single object
and structure on it. Also, the categorical semantics of DEL can be merged
straightforwardly with a standard categorical semantics for first-order logic,
providing a semantics for first-order DEL.Comment: In Proceedings TARK 2017, arXiv:1707.0825
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
Propositional dynamic logic for searching games with errors
We investigate some finitely-valued generalizations of propositional dynamic
logic with tests. We start by introducing the (n+1)-valued Kripke models and a
corresponding language based on a modal extension of {\L}ukasiewicz many-valued
logic. We illustrate the definitions by providing a framework for an analysis
of the R\'enyi - Ulam searching game with errors.
Our main result is the axiomatization of the theory of the (n+1)-valued
Kripke models. This result is obtained through filtration of the canonical
model of the smallest (n+1)-valued propositional dynamic logic
Model Checking Dynamic-Epistemic Spatial Logic
In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking
Some Epistemic Extensions of G\"odel Fuzzy Logic
In this paper, we introduce some epistemic extensions of G\"odel fuzzy logic
whose Kripke-based semantics have fuzzy values for both propositions and
accessibility relations such that soundness and completeness hold. We adopt
belief as our epistemic operator, then survey some fuzzy implications to
justify our semantics for belief is appropriate. We give a fuzzy version of
traditional muddy children problem and apply it to show that axioms of positive
and negative introspections and Truth are not necessarily valid in our basic
epistemic fuzzy models. In the sequel, we propose a derivation system as
a fuzzy version of classical epistemic logic . Next, we establish some other
epistemic-fuzzy derivation systems and which are
extensions of , and prove that all of these derivation systems are sound
and complete with respect to appropriate classes of Kripke-based models
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