Related papers: Characterizing Equivalence of Logically Constraine…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
Leftist grammars [Motwani et al., STOC 2000] are special semi-Thue systems where symbols can only insert or erase to their left. We develop a theory of leftist grammars seen as word transformers as a tool toward rigorous analyses of their…
We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…
We have recently begun a project to develop a more effective and efficient way to marshal inferences from background knowledge to facilitate deep natural language understanding. The meaning of a word is taken to be the entities,…
Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for…
This study examines the lexical and syntactic interventions of human and LLM proofreading aimed at improving overall intelligibility in identical second language writings, and evaluates the consistency of outcomes across three LLMs…
Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a…
Query answering under existential rules -- implications with existential quantifiers in the head -- is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query answering is also…
Large language models (LLMs) excel at semantic understanding, yet their ability to reconstruct internal structure from scrambled inputs remains underexplored. Sentence-level restoration is ill-posed for automated evaluation because multiple…
Semantic Similarity between two sentences can be defined as a way to determine how related or unrelated two sentences are. The task of Semantic Similarity in terms of distributed representations can be thought to be generating sentence…
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…
The rapid advancement of large language models (LLMs) demands robust, unbiased, and scalable evaluation methods. However, human annotations are costly to scale, model-based evaluations are susceptible to stylistic biases, and…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…