On an Intuitionistic Logic for Pragmatics

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justications and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the S4 modal translation, we give a denition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is dened and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, dened as a hypothesis that in some situation the truth of p is epistemically necessary

An algebraic semantics for QVT-relations check-only transformations

Fundamenta Informaticae, 114 1, Juan de Lara, Esther Guerra, An algebraic semantics for QVT-relations check-only transformations, 73-101, Copyright 2012, with permission from IOS PressQVT is the standard for model transformation defined by the OMG in the context of the Model-Driven Architecture. It is made of several transformation languages. Among them, QVT-Relations is the one with the highest level of abstraction, as it permits developing bidirectional transformations in a declarative, relational style. Unfortunately, the standard only provides a semiformal description of its semantics, which hinders analysis and has given rise to ambiguities in existing tool implementations. In order to improve this situation, we propose a formal, algebraic semantics for QVT-Relations check-only transformations, defining a notion of satisfaction of QVT-Relations specifications by models.This work has been supported by the Spanish Ministry of Science and Innovation with projects METEORIC (TIN2008-02081) and Go Lite (TIN2011-24139), and by the R&D program of the Community of Madrid with project “e-Madrid” (S2009/TIC-1650)

A syntax for semantics in P-Lingua

P-Lingua is a software framework for Membrane Computing, it includes a programming language, also called P-Lingua, for writting P system de nitions using a syntax close to standard scienti c notation. The rst line of a P-Lingua le is an unique identi er de ning the variant or model of P system to be used, i.e, the semantics of the P system. Software tools based on P-Lingua use this identi er to select a simulation algorithm implementing the corresponding derivation mode. Derivation modes de ne how to obtain a con guration Ct+1 from a con guration Ct. This information is usually hard-coded in the simulation algorithm. The P system model also de nes what types or rules can be used, the P-Lingua compiler uses the identi er to select an speci c parser for the le. In this case, a set of parsers is codi ed within the compiler tool. One for each unique identi er. P-Lingua has grown during the last 12 years, including more and more P system models. From a software engineering point of view, this approximation implies a continous development of the framework, leading to a monolithic software which is hard to debug and maintain. In this paper, we propose a new software approximation for the framework, including a new syntax for de ning rule patterns and derivation modes. The P-Lingua users can now de ne custom P system models instead of hard-coding them in the software. This approximation leads to a more exible solution which is easier to maintain and debug. Moreover, users could de ne and play with new/experimental P system models

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Other Buds in Membrane Computing

It is well-known the huge Mario’s contribution to the development of Membrane Computing. Many researchers may relate his name to the theory of complexity classes in P systems, the research of frontiers of the tractability or the application of Membrane Computing to model real-life situations as the Quorum Sensing System in Vibrio fischeri or the Bearded Vulture ecosystem. Beyond these research areas, in the last years Mario has presented many new research lines which can be considered as buds in the robust Membrane Computing tree. Many of them were the origin of new research branches, but some others are still waiting to be developed. This paper revisits some of these buds

Unifying Functional Interpretations: Past and Future

This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of functional interpretations, functional interpretations "with truth", and bounded functional interpretations. Our goal in the present paper is twofold: (1) to look back and single out the main lessons learnt so far, and (2) to look forward and list several open questions and possible directions for further research.Comment: 18 page