Permutative Additives and Exponentials
نویسنده
چکیده
Permutative logic (PL) is a noncommutative variant of multiplicative linear logic (MLL) arising from recent investigations concerning the topology of linear proofs. Permutative sequents are structured as oriented surfaces with boundary whose topological complexity is able to encode some information about the exchange in sequential proofs. In this paper we provide a complete permutative sequent calculus by extending that one of PL with rules for additives and exponentials. This extended system, here called permutative linear logic (PLL), is shown to be a conservative extension of linear logic and able to enjoy cut-elimination. Moreover, some basic isomorphisms are pointed out.
منابع مشابه
Count-Invariance Including Exponentials
We define infinitary count-invariance for categorial logic, extending countinvariance for multiplicatives (van Benthem, 1991) and additives and bracket modalities (Valentı́n et al., 2013) to include exponentials. This provides an e↵ective tool for pruning proof search in categorial parsing/theorem-proving.
متن کاملDecidability of Linear AÆne Logic
Propositional linear logic is known to be undecidable. In the current paper we prove that full propositional linear aÆne logic containing all the multiplicatives, additives, exponentials, and constants is decidable. The proof is based on a reduction of linear aÆne logic to sequents of speci c \normal forms", and on a generalization of Kanovich computational interpretation of linear logic adapte...
متن کاملRepresentations of the Cuntz - Krieger algebras . II — Permutative representations —
We generalize permutative representations of the Cuntz algebras for the Cuntz-Krieger algebra OA for any A. We characterize cyclic permutative representations by notions of cycle and chain, and show their existence and uniqueness. We show necessary and sufficient conditions for their irreducibility and equivalence. In consequence, we have a complete classification of permutative representations...
متن کاملUnification in Permutative Equational Theories is Undecidable
An equational theory E is permutative if for all terms s, t : s =E t implies that the terms s and t contain the same symbols with the same number of occurrences. The class of permutative equational theories includes the theory of AC (associativity and commutativity). It is shown in this research note that there is no algorithm that decides E-unifiability of terms for all permutative theories. T...
متن کاملUniversal fermionization of bosons on permutative representations of the Cuntz algebra O 2
Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra O2. As examples, we show fermionizations on the Fock space and the infinite wedge. Mathematics Subject Classifications (2000). 46K10, 46L60
متن کامل