Related papers: Some observations on the logical foundations of in…
The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
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…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…
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…
Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Automatic fake news detection models are ostensibly based on logic, where the truth of a claim made in a headline can be determined by supporting or refuting evidence found in a resulting web query. These models are believed to be reasoning…
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…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…