Related papers: Coming to Terms with Quantified Reasoning
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampires output. We describe ongoing efforts in reconstructing…
Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
Vampire has been for a long time the strongest first-order automatic theorem prover, widely used for hammer-style proof automation in ITPs such as Mizar, Isabelle, HOL, and Coq. In this work, we considerably improve the performance of…
We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n),…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
In this paper we demonstrate how logic programming systems and Automated first-order logic Theorem Provers (ATPs) can improve the accuracy of Large Language Models (LLMs) for logical reasoning tasks where the baseline performance is given…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…