Related papers: Logical Primes, Metavariables and Satisfiability

Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…

Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…

Large language models (LLMs) demonstrate considerable potential in various natural language tasks but face significant challenges in mathematical reasoning, particularly in executing precise, multi-step logic. However, current evaluation…

Large Language Models (LLMs) increasingly show reasoning rationales alongside their answers, turning "reasoning" into a user-interface element. While step-by-step rationales are typically associated with model performance, how they…

The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…

Financial forecasting increasingly uses large neural network models, but their opacity raises challenges for trust and regulatory compliance. We present several approaches to explainable and reliable AI in finance. \emph{First}, we describe…

This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

Large language models (LLMs) often generate content that contains factual errors when responding to fact-seeking prompts on open-ended topics. To benchmark a model's long-form factuality in open domains, we first use GPT-4 to generate…

We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with…

Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…

Counterfactual explanations (CFEs) are an emerging technique under the umbrella of interpretability of machine learning (ML) models. They provide ``what if'' feedback of the form ``if an input datapoint were $x'$ instead of $x$, then an ML…

The increasing use of Machine Learning (ML) software can lead to unfair and unethical decisions, thus fairness bugs in software are becoming a growing concern. Addressing these fairness bugs often involves sacrificing ML performance, such…

A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. We study phase transition in a context of matched formulas and their generalization of biclique satisfiable…

Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…

Modern LLMs can now produce highly readable abstractive summaries, to the point that traditional automated metrics for evaluating summary quality, such as ROUGE, have saturated. However, LLMs still sometimes introduce inaccuracies into…

While the reasoning capabilities of Large Language Models (LLMs) excel in analytical tasks such as mathematics and code generation, their utility for abstractive summarization remains widely assumed but largely unverified. To bridge this…

The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…