Related papers: A simplified framework for first-order languages a…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
This paper focuses on resolution in linguistic first order logic with truth value taken from linear symmetrical hedge algebra. We build the basic components of linguistic first order logic, including syntax and semantics. We present a…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It…
We report on our experiments to train deep neural networks that automatically translate informalized LaTeX-written Mizar texts into the formal Mizar language. To the best of our knowledge, this is the first time when neural networks have…
This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…