3 research outputs found
Annotation-Free Sequent Calculi for Full Intuitionistic Linear Logic -- Extended Version
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic
linear logic extended with par. Its proof theory has been notoriously difficult
to get right, and existing sequent calculi all involve inference rules with
complex annotations to guarantee soundness and cut-elimination. We give a
simple and annotation-free display calculus for FILL which satisfies Belnap's
generic cut-elimination theorem. To do so, our display calculus actually
handles an extension of FILL, called Bi-Intuitionistic Linear Logic (BiILL),
with an `exclusion' connective defined via an adjunction with par. We refine
our display calculus for BiILL into a cut-free nested sequent calculus with
deep inference in which the explicit structural rules of the display calculus
become admissible. A separation property guarantees that proofs of FILL
formulae in the deep inference calculus contain no trace of exclusion. Each
such rule is sound for the semantics of FILL, thus our deep inference calculus
and display calculus are conservative over FILL. The deep inference calculus
also enjoys the subformula property and terminating backward proof search,
which gives the NP-completeness of BiILL and FILL
Multi-type display calculus for Propositional Dynamic Logic
We introduce a multi-type display calculus for Propositional Dynamic Logic
(PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style
cut-elimination and subformula property.Comment: arXiv admin note: text overlap with arXiv:1805.0758
Multi-type Display Calculus for Dynamic Epistemic Logic
In the present paper, we introduce a multi-type display calculus for dynamic
epistemic logic, which we refer to as Dynamic Calculus. The display-approach is
suitable to modularly chart the space of dynamic epistemic logics on
weaker-than-classical propositional base. The presence of types endows the
language of the Dynamic Calculus with additional expressivity, allows for a
smooth proof-theoretic treatment, and paves the way towards a general
methodology for the design of proof systems for the generality of dynamic
logics, and certainly beyond dynamic epistemic logic. We prove that the Dynamic
Calculus adequately captures Baltag-Moss-Solecki's dynamic epistemic logic, and
enjoys Belnap-style cut elimination