Learning to Reason

Theorem proving formalizes the notion of deductive reasoning, while machine learning formalizes the notion of inductive reasoning. In this thesis, we present an overview of the current state of machine learning guided first-order automated theorem proving systems and outline a novel high-level modular object-oriented framework for combining arbitrary machine learning models with arbitrary proof calculi. Additionally, we present an example implementation in the aforementioned framework taking a novel approach to combining graph neural networks with the first-order connection calculus, generating a new Python implementation of the leanCoP theorem prover as a by-product

Rewriting Logic Semantics and Symbolic Analysis for Parametric Timed Automata

This paper presents a rewriting logic semantics for parametric timed automata (PTAs) and shows that symbolic reachability analysis using Maude-with-SMT is sound and complete for the PTA reachability problem. We then refine standard Maude-with-SMT reachability analysis so that the analysis terminates when the symbolic state space of the PTA is finite. We show how we can synthesize parameters with our methods, and compare their performance with Imitator, a state-of-the-art tool for PTAs. The practical contributions are twofold: providing new analysis methods for PTAs-e.g. allowing more general state properties in queries and supporting reachability analysis combined with user-defined execution strategies-not supported by Imitator, and developing symbolic analysis methods for real-time rewrite theories

Symbolic Analysis and Parameter Synthesis for Time Petri Nets Using Maude and SMT Solving

International audienc

Rewriting Logic Semantics and Symbolic Analysis for Parametric Timed Automata

This paper presents a rewriting logic semantics for parametric timed automata (PTAs) and shows that symbolic reachability analysis using Maude-with-SMT is sound and complete for the PTA reachability problem. We then refine standard Maude-with-SMT reachability analysis so that the analysis terminates when the symbolic state space of the PTA is finite. We show how we can synthesize parameters with our methods, and compare their performance with Imitator, a state-of-the-art tool for PTAs. The practical contributions are two-fold: providing new analysis methods for PTAs - -e.g. allowing more general state properties in queries and supporting reachability analysis combined with user-defined execution strategies - -not supported by Imitator, and developing symbolic analysis methods for real-time rewrite theories.1

Symbolic Analysis and Parameter Synthesis for Networks of Parametric Timed Automata with Global Variables using Maude and SMT Solving

International audienc