Hammering towards QED

This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a strong “one-stroke” tool for discharging difficult lemmas without the need for careful and detailed manual programming of proof search. The main ingredients underlying this approach are efficient automatic theorem provers that can cope with hundreds of axioms, suitable translations of the proof assistant’s logic to the logic of the automatic provers, heuristic and learning methods that select relevant facts from large libraries, and methods that reconstruct the automatically found proofs inside the proof assistants. We outline the history of these methods, explain the main issues and techniques, and show their strength on several large benchmarks. We also discuss the relation of this technology to the QED Manifesto and consider its implications for QED-like efforts.Blanchette’s Sledgehammer research was supported by the Deutsche Forschungs- gemeinschaft projects Quis Custodiet (grants NI 491/11-1 and NI 491/11-2) and Hardening the Hammer (grant NI 491/14-1). Kaliszyk is supported by the Austrian Science Fund (FWF) grant P26201. Sledgehammer was originally supported by the UK’s Engineering and Physical Sciences Research Council (grant GR/S57198/01). Urban’s work was supported by the Marie-Curie Outgoing International Fellowship project AUTOKNOMATH (grant MOIF-CT-2005-21875) and by the Netherlands Organisation for Scientific Research (NWO) project Knowledge-based Automated Reasoning (grant 612.001.208).This is the final published version. It first appeared at http://jfr.unibo.it/article/view/4593/5730?acceptCookies=1

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

Dynamic Generation of Interpretable Inference Rules in a Neuro-Symbolic Expert System

We present an approach for systematic reasoning that produces human interpretable proof trees grounded in a factbase. Our solution resembles the style of a classic Prolog-based inference engine, where we replace handcrafted rules through a combination of neural language modeling, guided generation, and semiparametric dense retrieval. This novel reasoning engine, NELLIE, dynamically instantiates interpretable inference rules that capture and score entailment (de)compositions over natural language statements. NELLIE provides competitive performance on scientific QA datasets requiring structured explanations over multiple facts

Working Notes from the 1992 AAAI Workshop on Automating Software Design. Theme: Domain Specific Software Design

The goal of this workshop is to identify different architectural approaches to building domain-specific software design systems and to explore issues unique to domain-specific (vs. general-purpose) software design. Some general issues that cut across the particular software design domain include: (1) knowledge representation, acquisition, and maintenance; (2) specialized software design techniques; and (3) user interaction and user interface

Fourth NASA Langley Formal Methods Workshop

This publication consists of papers presented at NASA Langley Research Center's fourth workshop on the application of formal methods to the design and verification of life-critical systems. Topic considered include: Proving properties of accident; modeling and validating SAFER in VDM-SL; requirement analysis of real-time control systems using PVS; a tabular language for system design; automated deductive verification of parallel systems. Also included is a fundamental hardware design in PVS