1,613 research outputs found
Proof Theory for Lax Logic
In this paper some proof theory for propositional Lax Logic is developed. A
cut free terminating sequent calculus is introduced for the logic, and based on
that calculus it is shown that the logic has uniform interpolation.
Furthermore, a separate, simple proof of interpolation is provided that also
uses the sequent calculus. From the literature it is known that Lax Logic has
interpolation, but all known proofs use models rather than proof systems
Uniform Interpolation for Coalgebraic Fixpoint Logic
We use the connection between automata and logic to prove that a wide class
of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first
we generalize one of the central results in coalgebraic automata theory, namely
closure under projection, which is known to hold for weak-pullback preserving
functors, to a more general class of functors, i.e.; functors with
quasi-functorial lax extensions. Then we will show that closure under
projection implies definability of the bisimulation quantifier in the language
of coalgebraic fixpoint logic, and finally we prove the uniform interpolation
theorem
Category theoretic semantics for theorem proving in logic programming: embracing the laxness
A propositional logic program may be identified with a -coalgebra
on the set of atomic propositions in the program. The corresponding
-coalgebra, where is the cofree comonad on ,
describes derivations by resolution. Using lax semantics, that correspondence
may be extended to a class of first-order logic programs without existential
variables. The resulting extension captures the proofs by term-matching
resolution in logic programming. Refining the lax approach, we further extend
it to arbitrary logic programs. We also exhibit a refinement of Bonchi and
Zanasi's saturation semantics for logic programming that complements lax
semantics.Comment: 20 pages, CMCS 201
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
A proof-theoretic analysis of the classical propositional matrix method
The matrix method, due to Bibel and Andrews, is a proof procedure designed for automated theorem-proving. We show that underlying this method is a fully structured combinatorial model of conventional classical proof theory. © 2012 The Author, 2012. Published by Oxford University Press
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