Related papers: Automating Induction by Reflection
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…
Induction is typically formalized as a rule or axiom extension of the LK-calculus. While this extension of the sequent calculus is simple and elegant, proof transformation and analysis can be quite difficult. Theories with an induction…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…
We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that…
An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…