Linear logic and noncommutativity in the calculus of structures
نویسنده
چکیده
منابع مشابه
Structures for Multiplicative Cyclic Linear Logic: Deepness vs Cyclicity
The aim of this work is to give an alternative presentation for the multiplicative fragment of Yetter’s cyclic linear logic. The new presentation is inspired by the calculus of structures, and has the interesting feature of avoiding the cyclic rule. The main point in this work is to show how cyclicity can be substituted by deepness, i.e. the possibility of applying an inference rule at any poin...
متن کاملNon-commutativity and MELL in the Calculus of Structures
We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a self-dual noncommutative operator inspired by CCS, that seems not to be expressible in the sequent calculus. Then we show that multiplicative exponential linear logic benefits from its...
متن کاملFocused Proof Search for Linear Logic in the Calculus of Structures
The proof-theoretic approach to logic programming has benefited from the introduction of focused proof systems, through the non-determinism reduction and control they provide when searching for proofs in the sequent calculus. However, this technique was not available in the calculus of structures, known for inducing even more non-determinism than other logical formalisms. This work in progress ...
متن کاملReducing Nondeterminism in the Calculus of Structures
The calculus of structures is a proof theoretical formalism which generalizes the sequent calculus with the feature of deep inference: in contrast to the sequent calculus, inference rules can be applied at any depth inside a formula, bringing shorter proofs than all other formalisms supporting analytical proofs. However, deep applicability of inference rules causes greater nondeterminism than i...
متن کاملNon-commutative logic II: sequent calculus and phase semantics
Non-commutative logic, which is an uniication of commutative linear logic and cyclic linear logic, is extended to all linear connectives: additives, exponentials and constants. We give two equivalent versions of the sequent calculus | directly with the structure of series-parallel order varieties, and with their presentations as partial orders |, phase semantics and a cut elimination theorem.
متن کامل