https://jfr.unibo.it/issue/feedJournal of Formalized Reasoning2018-10-31T13:32:59+01:00Prof. Andrea Aspertiasperti@cs.unibo.itOpen Journal Systems<strong>Journal of Formalized Reasoning (JFR) – ISSN 1972-5787</strong> encourages submission of papers describing significant, automated or semi-automated formalization efforts in any area, including classical mathematics, constructive mathematics, formal algorithms, and program verification. The emphasis of the journal is on proof techniques and methodologies and their impact on the formalization process. In particular, the journal provides a forum for comparing alternative approaches, enhancing reusability of solutions and offering a clear view of the current state of the field.https://jfr.unibo.it/article/view/7517Dependent Types for Extensive Games2018-10-29T11:32:40+01:00Pierre Lescannepierre.lescanne@ens-lyon.frExtensive games are tools largely used in economics to describe decision processes of a community of agents. In this paper we propose a formal presentation based on the proof assistant COQ which focuses mostly on infinite extensive games and their characteristics. COQ proposes a feature called "dependent types'', which means that the type of an object may depend on the type of its components. For instance, the set of choices or the set of utilities of an agent may depend on the agent herself. Using dependent types, we describe formally a very general class of games and strategy profiles, which corresponds somewhat to what game theorists are used to. We also discuss the notions of infiniteness in game theory and how this can be precisely described.2018-03-08T15:05:49+01:00Copyright (c) 2018 Pierre Lescannehttps://jfr.unibo.it/article/view/8212A Decision Procedure for Univariate Polynomial Systems Based on Root Counting and Interval Subdivision2018-10-31T13:32:59+01:00Anthony Joseph Narkawiczanthony.narkawicz@nasa.govCesar MunozCesar.A.Munoz@nasa.govAaron M. Dutleaaron.m.dutle@nasa.govThis paper presents a formally verified decision procedure for determinining the satisfiability of a system of univariate polynomial relations over the real line. The procedure combines a root counting function, based on Sturm’s theorem, with an interval subdivision algorithm. Given a system of polynomial relations over the same variable, the decision procedure progressively subdivides the real interval into smaller intervals. The subdivision continues until the satisfiability of the system can be determined on each subinterval using Sturm’s theorem on a subset of the system’s polynomials. The decision procedure has been formally verified in the Prototype Verification System (PVS). In PVS, the decision procedure is specified as a computable Boolean function on a deep embedding of polynomial relations. This function is used to define a proof producing strategy for automatically proving existential and universal statements on polynomial systems. The soundness of the strategy solely depends on the internal logic of PVS.2018-05-29T00:00:00+02:00Copyright (c) 2018 Cesar Munoz, Anthony Joseph Narkawicz, Aaron M. Dutlehttps://jfr.unibo.it/article/view/8124Formalization Techniques for Asymptotic Reasoning in Classical Analysis2018-10-29T12:24:10+01:00Reynald Affeldtreynald.affeldt@aist.go.jpCyril Cohencyril.cohen@inria.frDamien Rouhlingdamien.rouhling@inria.fr<p>Formalizing analysis on a computer involves a lot of “epsilon-delta” reasoning, while informal reasoning may use some asymptotical hand-waving. Whether or not the arithmetic details are hidden using some abstraction like filters, a human user eventually has to break it down for the proof assistant anyway, and provide a witness for the existential variable “delta”. We describe formalization techniques that take advantage of existential variables to delay the input of witnesses until a stage where the proof assistant can actually infer them. We use these techniques to prove theorems about classical analysis and to provide equational Bachmann-Landau notations. This partially restores the simplicity of informal hand-waving without compromising the proof. As expected this also reduces the size of proof scripts and the time to write them, and it also makes proofs more stable.</p>2018-10-29T11:24:34+01:00Copyright (c) 2018 Reynald Affeldt, Cyril Cohen, Damien Rouhling