Related papers: Extending E Prover with Similarity Based Clause Se…
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning. While simple and effective, adding theory axioms can also pollute the search space with many irrelevant…
This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a…
Clause selection is arguably the most important choice point in saturation-based theorem proving. Framing it as a reinforcement learning (RL) task is a way to challenge the human-designed heuristics of state-of-the-art provers and to…
We re-examine the topic of machine-learned clause selection guidance in saturation-based theorem provers. The central idea, recently popularized by the ENIGMA system, is to learn a classifier for recognizing clauses that appeared in…
The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
Fact verification systems typically rely on neural network classifiers for veracity prediction which lack explainability. This paper proposes ProoFVer, which uses a seq2seq model to generate natural logic-based inferences as proofs. These…
Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…
We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach. Unlike in the first ENIGMA implementation where fast linear classifier is trained and used together with…
As recommendation is essentially a comparative (or ranking) process, a good explanation should illustrate to users why an item is believed to be better than another, i.e., comparative explanations about the recommended items. Ideally, after…
Proof search in non-confluent tableau calculi, such as the connection tableau calculus, suffers from excess backtracking, but simple restrictions on backtracking are incomplete. We adopt constraint learning to reduce backtracking in the…