Linear Logic and Exceptions

Fouqueré, Christophe; Vauzeilles, Jacqueline

doi:10.1093/logcom/4.6.859

Cited by 5 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The logical platform of CSI is that of multiplicative linear logic [6]. In this sense, this calculus is not the first attempt to encode non-monotonic patterns of inference by means of linear logic [4,3]. However, CSI is a first proposal for representing processes involving context-sensitive interactions (so the acronym), which prompt for a controlled monotonicity of the ⊗-conjunction.…”

Section: A B a C B C A B C A C Bmentioning

confidence: 99%

See 1 more Smart Citation

A logical calculus for controlled monotonicity

D’Agostino

Piazza

Pulcini

2014

Journal of Applied Logic

View full text Add to dashboard Cite

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes

show abstract

Section: A B a C B C A B C A C Bmentioning

confidence: 99%

“…Moreover, it would be interesting to encode semantic networks with exceptions [5] by means of the σCSI calculus. With respect to linear logic this has been done in [4,3]. In this way, we would reach a better grasp of the relations holding between our deductive system and standard default logics [8].…”

Section: Conclusion and Further Workmentioning

confidence: 99%

A logical calculus for controlled monotonicity

D’Agostino

Piazza

Pulcini

2014

Journal of Applied Logic

View full text Add to dashboard Cite

show abstract

“…9 The linear implication --o : A --o B means "if the resource A was available, then the computation could go to state B." )1 : Unlike the Negation As Failure para-digm, linear negation is an involution satisfying De Morgan-like properties.…”

Section: 1mentioning

confidence: 99%

Linear logic for deductive databases

Lee

Tsang

1999

New Gener Comput

View full text Add to dashboard Cite

This paper deals with deductive databases in linear logic. The semantics of queries, views, constraints, and (view) updates are defined deelaratively in linear logic. In contrast to classical logic, we can formalise non-shared view, transition constraints, and (view) updates easily. Various proof search strategies are presented along with an algorithm for query evaluation from a bottom-up direction. An additional advantage is that the associated meaning of a given relation can be defined in terms of the validity of a legal update in a given relation. We also defined formally the update principles and showed the correctness of the update translation algorithms. In this approach, we provide virtual view updates along with real view updates, and view DELETIONs are special cases of view REPLACEMENTs. This permits three transactional view update operations (INSERTION, DELETION, RE-PLACEMENT) in comparison to only (INSERTION, DELETION) in most existing systems.

show abstract