Algorithmic specifications in linear logic with subexponentials

Se detectó que no hubo un seguimiento de cobranza por parte de las áreas de crédito y cobranza , que no existe un control ni política de cobranza , por lo tanto su cuenta por cobrar es muy elevado con un importe de 57,864.00 soles ; se le recomienda que implemente una política y control de cobranza y identificar a los cliente que ya tienen más de un año sin pagar , con el motivo de aplicar un asiento contable y que nos permita tomarlo como gasto con el motivo de poder reducir la cuenta , La empresa, debe hacer un seguimiento de los créditos concedidos a 30,60 y 90, y agilizar el cobro de sus cuentas. Esto le permitiría que la empresa pueda tener a detalle de los clientes que tienen pendientes por cobrar y evitar un nuevo servicio.It was detected that there was no collection follow-up by the credit and collection areas, that there is no control or collection policy, therefore your account receivable is very high with an amount of 57,864.00 soles; It is recommended that you implement a collection policy and control and identify customers who have been paying for more than one year, with the purpose of applying an accounting entry and allowing us to take it as an expense in order to reduce the account, The company must follow up on the credits granted to 30.60 and 90, and expedite the collection of their accounts. This would allow the company to have details of the customers who have outstanding receivables and avoid a new service.Trabajo de investigació

Undecidability of Multiplicative Subexponential Logic

Subexponential logic is a variant of linear logic with a family of exponential connectives--called subexponentials--that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that classical propositional multiplicative linear logic extended with one unrestricted and two incomparable linear subexponentials can encode the halting problem for two register Minsky machines, and is hence undecidable.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441

Expressing Additives Using Multiplicatives and Subexponentials

International audienceSubexponential logic is a variant of linear logic with a family of exponential connectives—called subex-ponentials—that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that a classical propositional multiplicative subexponential logic (MSEL) with one unrestricted and two linear subexponentials can encode the halting problem for two register Minsky machines, and is hence undecidable. We then show how the additive con-nectives can be directly simulated by giving an encoding of propositional multiplicative additive linear logic (MALL) in an MSEL with one unrestricted and four linear subexponentials

On Subexponentials, Synthetic Connectives, and Multi-level Delimited Control

International audienceWe construct a partially-ordered hierarchy of delimited control operators similar to those of the CPS hierarchy of Danvy and Filinski. However, instead of relying on nested CPS translations, these operators are directly interpreted in linear logic extended with subexponentials (i.e., multiple pairs of ! and ?). We construct an independent proof theory for a fragment of this logic based on the principle of focusing. It is then shown that the new constraints placed on the permutation of cuts correspond to multiple levels of delimited control

An adequate compositional encoding of bigraph structure in linear logic with subexponentials

International audienceIn linear logic, formulas can be split into two sets: classical (those that can be used as many times as necessary) or linear (those that are consumed and no longer available after being used). Subexponentials generalize this notion by allowing the formulas to be split into many sets, each of which can then be specified to be classical or linear. This flexibility increases its expressiveness: we already have adequate encodings of a number of other proof systems, and for computational models such as concurrent constraint programming, in linear logic with subexponentials (SEL). Bigraphs were proposed by Milner in 2001 as a model for ubiquitous computing, subsuming models of computation such as CCS and the π-calculus and capable of modeling connectivity and locality at the same time. In this work we present an encoding of the bigraph structure in SEL, thus giving an indication of the expressive power of this logic, and at the same time providing a framework for reasoning and operating on bigraphs. Our encoding is adequate and therefore the operations of composition and juxtaposition can be performed on the logical level. Moreover, all the proof-theoretical tools of SEL become available for querying and proving properties of bigraph structures

A system of inference based on proof search: an extended abstract

Gentzen designed his natural deduction proof system to ``come as close as possible to actual reasoning.'' Indeed, natural deduction proofs closely resemble the static structure of logical reasoning in mathematical arguments. However, different features of inference are compelling to capture when one wants to support the process of searching for proofs. PSF (Proof Search Framework) attempts to capture these features naturally and directly. The design and metatheory of PSF are presented, and its ability to specify a range of proof systems for classical, intuitionistic, and linear logic is illustrated

Hybrid and Subexponential Linear Logics Technical Report

HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL) as a common ground and they admit (cut-free) complete focused proof systems. The difference between the two logics relies on the way modalities are handled. In HyLL, truth judgments are labelled by worlds and hybrid connectives relate worlds with formulas. In SELL, the linear logic exponentials (!, ?) are decorated with labels representing locations, and an ordering on such labels defines the provability relation among resources in those locations. It is well known that SELL, as a logical framework, is strictly more expressive than LL. However, so far, it was not clear whether HyLL is more expressive than LL and/or SELL. In this paper, we show an encoding of the HyLL's logical rules into LL with the highest level of adequacy, hence showing that HyLL is as expressive as LL. We also propose an encoding of HyLL into SELL ⋓ (SELL plus quantification over locations) that gives better insights about the meaning of worlds in HyLL. We conclude our expressiveness study by showing that previous attempts of encoding Computational Tree Logic (CTL) operators into HyLL cannot be extended to consider the whole set of temporal connectives. We show that a system of LL with fixed points is indeed needed to faithfully encode the behavior of such temporal operators