Importing SMT and Connection proofs as expansion trees

Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and then study the language used to represent proofs, on a prover by prover basis. In this work we present an implementation that takes SMT and Connection proof objects from two different provers and imports them both as expansion trees. By representing the proofs in the same framework, all the algorithms and tools available for expansion trees (compression, visualization, sequent calculus proof construction, proof checking, etc.) can be employed uniformly. The expansion proofs can also be used as a validation tool for the proof objects produced.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

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

Introducing Quantified Cuts in Logic with Equality

Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method generating lemmas of the form $\forall x_1\ldots\forall x_n.A$. Moreover, we extend the original method to predicate logic with equality. The new method was implemented and applied to the TSTP proof database. It is shown that the extension of the method to handle equality and quantifier-blocks leads to a substantial improvement of the old algorithm

The Proof Certifier Checkers

International audienceDifferent theorem provers work within different formalisms and paradigms, and therefore produce various incompatible proof objects. Currently there is a big effort to establish foundational proof certificates (FPC), which would serve as a common " specification language " for all these formats. Such framework enables the uniform checking of proof objects from many different theorem provers while relying on a small and trusted kernel to do so. Checkers is an implementation of a proof checker using foundational proof certificates. By trusting a small kernel based on (focused) sequent calculus on the one hand and by supporting FPC specifications in a prolog-like language on the other hand, it can be used for checking proofs of a wide range of theorem provers. The focus of this paper is on the output of equational resolution theorem provers and for this end, we specify the paramodulation rule. We describe the architecture of Checkers and demonstrate how it can be used to check proof objects by supplying the FPC specification for a subset of the inferences used by E-prover and checking proofs using these inferences

The ILLTP Library for Intuitionistic Linear Logic

Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems in the traditional monograph "Introduction to Metamathematics". We analyze four different translations of intuitionistic logic into linear logic and compare their proofs using a linear logic based prover with focusing. In order to enhance the set of problems in our library, we apply the three provability-preserving translations to the propositional benchmarks in the ILTP Library. Finally, we generate a comprehensive set of reachability problems for Petri nets and encode such problems as linear logic sequents, thus enlarging our collection of problems

Quando diferentes maneiras de cuidar se tornam problema: o ofício descuidado, uma experiência com a metodologia de instrução ao sósia

This article summarizes an intervention conducted with caregivers of people with intellectual disabilities in a private organization in Minas Gerais, Brazil, with the approach of the Activity Clinic and which subsequently led to a research for a doctorate by the author in Occupational Psychology. The intervention took place with six caregivers, between 2010 and 2011, under the principles of Vygotski's historical and developmental methodology, associated to the method of instruction to the double. The content analysis of the dialogue was adopted, inspired by works of authors in the area and guided by the dialectical relation between activity and profession. In addition to the many evidences that a methodological framework could be installed, leading the caregivers to discuss the raised issues, two main results were selected to emphasize the methodological potential of the instruction to the double: the development of the activity of a caregiver, illustrated by an excerpt of the dialogues, and the arguments that indicate the absence (dysfunction) of the psychological function of the work collective (the professional genre) for those professionals.Este artigo resume uma intervenção realizada com os cuidadores de pessoas com deficiências intelectuais em uma organização privada, em Minas Gerais, sob a abordagem da Clínica da Atividade e que, posteriormente, originou a pesquisa para o doutorado da autora em Psicologia do Trabalho. A intervenção aconteceu com seis cuidadores, entre 2010 e 2011, sob os princípios da metodologia histórico-desenvolvimental de Vygotsky, associados ao método de instrução ao sósia. Adotou-se a análise de conteúdo dos diálogos, inspirada em trabalhos de autores da área, orientada pela relação dialética entre a atividade e o ofício. Além das várias evidências de que um enquadre metodológico pôde ser instalado, levando-os a discutir sobre a problemática posta, foram selecionados dois resultados que enfatizam o potencial metodológico da instrução ao sósia: o desenvolvimento da atividade de um cuidador, ilustrado por um trecho extraído dos diálogos, e os argumentos que indicam a ausência (disfunção) da função psicológica do coletivo de trabalho (o gênero profissional) para aqueles profissionais