A Tour on Ecumenical Systems

Ecumenism can be understood as a pursuit of unity, where diverse thoughts, ideas, or points of view coexist harmoniously. In logic, ecumenical systems refer, in a broad sense, to proof systems for combining logics. One captivating area of research over the past few decades has been the exploration of seamlessly merging classical and intuitionistic connectives, allowing them to coexist peacefully. In this paper, we will embark on a journey through ecumenical systems, drawing inspiration from Prawitz' seminal work [35]. We will begin by elucidating Prawitz' concept of “ecumenism” and present a pure sequent calculus version of his system. Building upon this foundation, we will expand our discussion to incorporate alethic modalities, leveraging Simpson's meta-logical characterization. This will enable us to propose several proof systems for ecumenical modal logics. We will conclude our tour with some discussion towards a term calculus proposal for the implicational propositional fragment of the ecumenical logic, the quest of automation using a framework based in rewriting logic, and an ecumenical view of proof-theoretic semantics

07421 Abstracts Collection -- Formal Protocol Verification Applied

From 14/10/2007 to 19/10/2007, the Dagstuhl Seminar 07421 ``Formal Protocol Verification Applied\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Combination of convex theories: Modularity, deduction completeness, and explanation

AbstractDecision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple “sat/unsat” answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson–Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories

07401 Abstracts Collection -- Deduction and Decision Procedures

From 01.10. to 05.10.2007, the Dagstuhl Seminar 07401 ``Deduction and Decision Procedures\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper

Finitary Deduction Systems

Cryptographic protocols are the cornerstone of security in distributed systems. The formal analysis of their properties is accordingly one of the focus points of the security community, and is usually split among two groups. In the first group, one focuses on trace-based security properties such as confidentiality and authentication, and provides decision procedures for the existence of attacks for an on-line attackers. In the second group, one focuses on equivalence properties such as privacy and guessing attacks, and provides decision procedures for the existence of attacks for an offline attacker. In all cases the attacker is modeled by a deduction system in which his possible actions are expressed. We present in this paper a notion of finitary deduction systems that aims at relating both approaches. We prove that for such deduction systems, deciding equivalence properties for on-line attackers can be reduced to deciding reachability properties in the same setting.Comment: 30 pages. Work begun while in the CASSIS Project, INRIA Nancy Grand Es

Proceedings of the Automated Reasoning Workshop (ARW 2019)

Preface This volume contains the proceedings of ARW 2019, the twenty sixths Workshop on Automated Rea- soning (2nd{3d September 2019) hosted by the Department of Computer Science, Middlesex University, England (UK). Traditionally, this annual workshop which brings together, for a two-day intensive pro- gramme, researchers from different areas of automated reasoning, covers both traditional and emerging topics, disseminates achieved results or work in progress. During informal discussions at workshop ses- sions, the attendees, whether they are established in the Automated Reasoning community or are only at their early stages of their research career, gain invaluable feedback from colleagues. ARW always looks at the ways of strengthening links between academia, industry and government; between theoretical and practical advances. The 26th ARW is affiliated with TABLEAUX 2019 conference. These proceedings contain forteen extended abstracts contributed by the participants of the workshop and assembled in order of their presentations at the workshop. The abstracts cover a wide range of topics including the development of reasoning techniques for Agents, Model-Checking, Proof Search for classical and non-classical logics, Description Logics, development of Intelligent Prediction Models, application of Machine Learning to theorem proving, applications of AR in Cloud Computing and Networking. I would like to thank the members of the ARW Organising Committee for their advice and assis- tance. I would also like to thank the organisers of TABLEAUX/FroCoS 2019, and Andrei Popescu, the TABLEAUX Conference Chair, in particular, for the enormous work related to the organisation of this affiliation. I would also like to thank Natalia Yerashenia for helping in preparing these proceedings. London Alexander Bolotov September 201

Satisfiability of General Intruder Constraints with and without a Set Constructor

Many decision problems on security protocols can be reduced to solving so-called intruder constraints in Dolev Yao model. Most constraint solving procedures for protocol security rely on two properties of constraint systems called monotonicity and variable origination. In this work we relax these restrictions by giving a decision procedure for solving general intruder constraints (that do not have these properties) that stays in NP. Our result extends a first work by L. Mazar\'e in several directions: we allow non-atomic keys, and an associative, commutative and idempotent symbol (for modeling sets). We also discuss several new applications of the results.Comment: Submitted to the Special issue of Information and Computation on Security and Rewriting Techniques (SecReT), 2011. 59 page

On metric temporal description logics

We introduce metric temporal description logics (mTDLs) as combinations of the classical description logic ALC with (a) LTLbin, an extension of the temporal logic LTL with succinctly represented intervals, and (b) metric temporal logic MTL, extending LTLbin with capabilities to quantitatively reason about time delays. Our main contributions are algorithms and tight complexity bounds for the satisfiability problem in these mTDLs: For mTDLs based on (fragments of) LTLbin, we establish complexity bounds ranging from EXPTIME to 2EXPSPACE. For mTDLs based on (fragments of) MTL interpreted over the naturals, we establish complexity bounds ranging from EXPSPACE to 2EXPSPACE