Related papers: Encoding TLA+ set theory into many-sorted first-or…
Lambda Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.
In this paper a class of languages which are formal enough for mathematical reasoning is introduced. First-order formal languages containing natural numbers and numerals belong to that class. Its languages are called mathematically…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…
LLMs are becoming increasingly capable and widespread. Consequently, the potential and reality of their misuse is also growing. In this work, we address the problem of detecting LLM-generated text that is not explicitly declared as such. We…
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…
This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When…
We describe an extension to the TLA+ specification language with constructs for writing proofs and a proof environment, called the Proof Manager (PM), to checks those proofs. The language and the PM support the incremental development and…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
Constraint answer set programming integrates answer set programming with constraint processing. System EZSMT+ is a constraint answer set programming tool that utilizes satisfiability modulo theory solvers for search. Its theoretical…
In the realm of Sign Language Translation (SLT), reliance on costly gloss-annotated datasets has posed a significant barrier. Recent advancements in gloss-free SLT methods have shown promise, yet they often largely lag behind gloss-based…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…