25 research outputs found
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Tools and Algorithms for the Construction and Analysis of Systems
This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
ProverX: rewriting and extending prover9
O propósito principal deste projecto é tornar o demonstrador automático de teoremas Prover9
programável e, por conseguinte, extensível.
Este propósito foi conseguido acrescentando um interpretador de Python, uma linha de comandos e
uma biblioteca de módulos, objectos e funções escritos em Python para interagir com ficheiros de
Prover9 e Mace4. Foi também criada uma “interface” gráfica de utilizador (GUI) sob a forma de uma
aplicação web para trazer aos utilizadores um meio mais eficiente e rápido de trabalhar com
demonstrações automáticas de teoremas.
A nova biblioteca de “scripting” oferece aos utilizadores novas funcionalidades tais como correr
várias sessões simultâneas de Prover9 parando automaticamente quando uma demonstração (ou um
contraexemplo) é encontrada, elaborar estratégias para aumentar a velocidade com que as
demonstrações são encontradas ou diminuir o tamanho das mesmas. Outro módulo permite interagir
com o sistema de álgebra GAP.
Sobre esta biblioteca, muitas outras funcionalidades podem ser facilmente acrescentadas pois o
objectivo principal é dar aos utilizadores a capacidade de acrescentar novas funcionalidades ao
Prover9.
Resumindo, o objectivo deste projecto é oferecer à comunidade matemática um ambiente integrado
para trabalhar com demonstração automática de teoremas.The primary purpose of this project is to extend Prover9 with a scripting language.
This was achieved by adding a Python interpreter, an interactive command line and a special
scripting library to interact with Prover9 and Mace4 files. A user interface in the form of a web
application was also created to help users achieve a more rapid and efficient way of working with
automated theorem proving.
The new scripting library offers utilities that allows a user to run several Prover9 sessions
concurrently and to create strategies for increasing the effectiveness of the proof search or to search
for shorter proofs. Another module allows to interact with the algebra system GAP.
Based on the library, many more functionalities can be easily added, as the main goal is to give users
the ability to extend the functionality of Prover9 the way they see fit.
In conclusion, the aim of this project is to offer to the mathematical community an integrated
environment for working with automated reasonin
31ème Journées Francophones des Langages Applicatifs
International audienc
The Lean mathematical library
This paper describes mathlib, a community-driven effort to build a unified
library of mathematics formalized in the Lean proof assistant. Among proof
assistant libraries, it is distinguished by its dependently typed foundations,
focus on classical mathematics, extensive hierarchy of structures, use of
large- and small-scale automation, and distributed organization. We explain the
architecture and design decisions of the library and the social organization
that has led us here
Automated Theorem Proving with Extensions of First-Order Logic
Automated theorem provers are computer programs that check whether a logical conjecture follows from a set of logical statements. The conjecture and the statements are expressed in the language of some formal logic, such as first-order logic. Theorem provers for first-order logic have been used for automation in proof assistants, verification of programs, static analysis of networks, and other purposes. However, the efficient usage of these provers remains challenging. One of the challenges is the complexity of translating domain problems to first-order logic. Not only can such translation be cumbersome due to semantic differences between the domain and the logic, but it might inadvertently result in problems that provers cannot easily handle.The work presented in the thesis addresses this challenge by developing an extension of first-order logic named FOOL. FOOL contains syntactical features of programming languages and more expressive logics, is friendly for translation of problems from various domains, and can be efficiently supported by existing theorem provers. We describe the syntax and semantics of FOOL and present a simple translation from FOOL to plain first-order logic. We describe an efficient clausal normal form transformation algorithm for FOOL and based on it implement a support for FOOL in the Vampire theorem prover. We illustrate the efficient use of FOOL for program verification by describing a concise encoding of next state relations of imperative programs in FOOL. We show a usage of features of FOOL in problems of static analysis of networks. We demonstrate the efficiency of automated theorem proving in FOOL with an extensive set of experiments. In these experiments we compare the performance of Vampire on a large collection of problems from various sources translated to FOOL and ordinary first-order logic. Finally, we fix the syntax for FOOL in TPTP, the standard language of first-order theorem provers