15,889 research outputs found
A Sequent Calculus for Modelling Interferences
A logic calculus is presented that is a conservative extension of linear
logic. The motivation beneath this work concerns lazy evaluation, true
concurrency and interferences in proof search. The calculus includes two new
connectives to deal with multisequent structures and has the cut-elimination
property. Extensions are proposed that give first results concerning our
objectives
Non-normal modalities in variants of Linear Logic
This article presents modal versions of resource-conscious logics. We
concentrate on extensions of variants of Linear Logic with one minimal
non-normal modality. In earlier work, where we investigated agency in
multi-agent systems, we have shown that the results scale up to logics with
multiple non-minimal modalities. Here, we start with the language of
propositional intuitionistic Linear Logic without the additive disjunction, to
which we add a modality. We provide an interpretation of this language on a
class of Kripke resource models extended with a neighbourhood function: modal
Kripke resource models. We propose a Hilbert-style axiomatization and a
Gentzen-style sequent calculus. We show that the proof theories are sound and
complete with respect to the class of modal Kripke resource models. We show
that the sequent calculus admits cut elimination and that proof-search is in
PSPACE. We then show how to extend the results when non-commutative connectives
are added to the language. Finally, we put the logical framework to use by
instantiating it as logics of agency. In particular, we propose a logic to
reason about the resource-sensitive use of artefacts and illustrate it with a
variety of examples
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
Classical BI: Its Semantics and Proof Theory
We present Classical BI (CBI), a new addition to the family of bunched logics
which originates in O'Hearn and Pym's logic of bunched implications BI. CBI
differs from existing bunched logics in that its multiplicative connectives
behave classically rather than intuitionistically (including in particular a
multiplicative version of classical negation). At the semantic level,
CBI-formulas have the normal bunched logic reading as declarative statements
about resources, but its resource models necessarily feature more structure
than those for other bunched logics; principally, they satisfy the requirement
that every resource has a unique dual. At the proof-theoretic level, a very
natural formalism for CBI is provided by a display calculus \`a la Belnap,
which can be seen as a generalisation of the bunched sequent calculus for BI.
In this paper we formulate the aforementioned model theory and proof theory for
CBI, and prove some fundamental results about the logic, most notably
completeness of the proof theory with respect to the semantics.Comment: 42 pages, 8 figure
Linear Time Logics - A Coalgebraic Perspective
We describe a general approach to deriving linear time logics for a wide
variety of state-based, quantitative systems, by modelling the latter as
coalgebras whose type incorporates both branching behaviour and linear
behaviour. Concretely, we define logics whose syntax is determined by the
choice of linear behaviour and whose domain of truth values is determined by
the choice of branching, and we provide two equivalent semantics for them: a
step-wise semantics amenable to automata-based verification, and a path-based
semantics akin to those of standard linear time logics. We also provide a
semantic characterisation of the associated notion of logical equivalence, and
relate it to previously-defined maximal trace semantics for such systems.
Instances of our logics support reasoning about the possibility, likelihood or
minimal cost of exhibiting a given linear time property. We conclude with a
generalisation of the logics, dual in spirit to logics with discounting, which
increases their practical appeal in the context of resource-aware computation
by incorporating a notion of offsetting.Comment: Major revision of previous version: Sections 4 and 5 generalise the
results in the previous version, with new proofs; Section 6 contains new
result
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