405 research outputs found
Embedding Kozen-Tiuryn Logic into Residuated One-Sorted Kleene Algebra with Tests
Kozen and Tiuryn have introduced the substructural logic for
reasoning about correctness of while programs (ACM TOCL, 2003). The logic
distinguishes between tests and partial correctness assertions,
representing the latter by special implicational formulas. Kozen and Tiuryn's
logic extends Kleene altebra with tests, where partial correctness assertions
are represented by equations, not terms. Kleene algebra with codomain,
, is a one-sorted alternative to Kleene algebra with tests that
expands Kleene algebra with an operator that allows to construct a Boolean
subalgebra of tests. In this paper we show that Kozen and Tiuryn's logic embeds
into the equational theory of the expansion of with residuals of
Kleene algebra multiplication and the upper adjoint of the codomain operator
Kleene Algebras, Regular Languages and Substructural Logics
We introduce the two substructural propositional logics KL, KL+, which use
disjunction, fusion and a unary, (quasi-)exponential connective. For both we
prove strong completeness with respect to the interpretation in Kleene algebras
and a variant thereof. We also prove strong completeness for language models,
where each logic comes with a different interpretation. We show that for both
logics the cut rule is admissible and both have a decidable consequence
relation.Comment: In Proceedings GandALF 2014, arXiv:1408.556
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
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