Related papers: Automatic Generation of Proof Tactics for Finite-V…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of…
We focus on a type of linguistic formal reasoning where the goal is to reason over explicit knowledge in the form of natural language facts and rules (Clark et al., 2020). A recent work, named PRover (Saha et al., 2020), performs such…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
While logical reasoning evaluation of Large Language Models (LLMs) has attracted significant attention, existing benchmarks predominantly rely on multiple-choice formats that are vulnerable to random guessing, leading to overestimated…
Hofmann (1999) introduced the functional programming language LFPL to characterize the functions computable in polynomial time using an affine type system. LFPL enables a natural programming style, including nested recursion, and has…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
In a previously published ENTCS paper (Santos et al. (2016)), we introduced a sequent calculus called $\mathbf{LMT^{\rightarrow}}$ for Minimal Implicational Propositional Logic ($\mathbf{LMT^{\rightarrow}}$). This calculus provides a proof…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
This paper presents FASTFOOD, a rule-based Natural Language Generation Program for cooking recipes. Recipes are generated by using an Automated Theorem Proving procedure to select the ingredients and instructions, with ingredients…
Presented, in this monograph, are the results of the U. S. Naval Academy Mathematical Logic Course Project. The propositional and predicate calculus is presented in a unique manner. All aspects are rigorously established using the the…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…