11,091 research outputs found
An elementary proof of the completeness of PDL
AbstractWe give an elementary proof of the completeness of the Segerberg axions for Propositional Dynamic Logic
Kleene Algebra with Dynamic Tests: Completeness and Complexity
We study versions of Kleene algebra with dynamic tests, that is, extensions
of Kleene algebra with domain and antidomain operators. We show that Kleene
algebras with tests and Propositional dynamic logic correspond to special cases
of the dynamic test framework. In particular, we establish completeness results
with respect to relational models and guarded-language models, and we show that
two prominent classes of Kleene algebras with dynamic tests have an
EXPTIME-complete equational theory
On Modal Logics of Partial Recursive Functions
The classical propositional logic is known to be sound and complete with
respect to the set semantics that interprets connectives as set operations. The
paper extends propositional language by a new binary modality that corresponds
to partial recursive function type constructor under the above interpretation.
The cases of deterministic and non-deterministic functions are considered and
for both of them semantically complete modal logics are described and
decidability of these logics is established
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Logics of Imprecise Comparative Probability
This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures
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
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