On Structuring Proof Search for First Order Linear Logic

Paola Bruscoli; Alessio Guglielmi

doi:10.1016/j.tcs.2005.11.047

Home/Archive/arXiv

arXiv · cs/0312002

On Structuring Proof Search for First Order Linear Logic

Paola Bruscoli·Alessio Guglielmi

View original source ↗Read source document ↗Export metadata ↓

Abstract

Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to deal with syntactic details that would normally be ignored by a reasonable operational semantics. In this respect, Forum improves on Gentzen systems for linear logic by restricting the language and the form of inference rules. We further improve on Forum by restricting the class of formulae allowed, in a system we call G-Forum, which is still equivalent to full first order linear logic. The only formulae allowed in G-Forum have the same shape as Forum sequents: the restriction does not diminish expressiveness and makes G-Forum amenable to proof theoretic analysis. G-Forum consists of two (big) inference rules, for which we show a cut elimination procedure. This does not need to appeal to finer detail in formulae and sequents than is provided by G-Forum, thus successfully testing the internal symmetries of our system.

Explore related subjects

cs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Paola Bruscoli, Alessio Guglielmi. 2003-12-01. On Structuring Proof Search for First Order Linear Logic. https://doi.org/10.1016/j.tcs.2005.11.047

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Probabilistic Choreography Language for PRISM

We present a choreographic framework for modelling and analysing concurrent probabilistic systems based on the PRISM model-checker. This is achieved through the development of a choreography language, which is a specification language that allows to describe the desired interactions within a concurrent system from a global viewpoint. Using choreographies gives a clear and complete view of system interactions, making it easier to understand the process flow and identify potential errors, which helps ensure correct execution and improves system reliability. We equip our language with a probabilistic semantics and then define a formal encoding into the PRISM language and discuss its correctness. Properties of programs written in our choreographic language can be model-checked by the PRISM model-checker via their translation into the PRISM language. Finally, we implement a compiler for our language and demonstrate its practical applicability via examples drawn from the use cases featured in the PRISM website.

cs.LO↗

arXiv2026

Monotone weak distributive laws over the lifted powerset monad in categories of algebras

Noticing the similarity between the monotone weak distributive laws combining two layers of nondeterminism in sets and in compact Hausdorff spaces, we study whether the latter law can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras: we then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.

cs.LO↗

arXiv2026

Identifying and Explaining (Non-)Equivalence of First-Order Logic Formulas

First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for (non-)equivalence and to provide explanations for non-equivalence. We propose such methods based on both theoretical insights and existing tools, implement them, and report on experiments testing their effectiveness on a large educational data set with > 100,000 pairs of first-order formulas.

cs.LO↗