Related papers: First-Order Logic in Finite Domains: Where Semanti…
Translating formulas of Linear Temporal Logic (LTL) over finite traces, or LTLf, to symbolic Deterministic Finite Automata (DFA) plays an important role not only in LTLf synthesis, but also in synthesis for Safety LTL formulas. The…
Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
We present a number of first- and second-order extensions to SMT theories specifically aimed at representing and analyzing SQL queries with join, projection, and selection operations. We support reasoning about SQL queries with either bag…
Semantic Role Labeling (SRL) aims at recognizing the predicate-argument structure of a sentence and can be decomposed into two subtasks: predicate disambiguation and argument labeling. Prior work deals with these two tasks independently,…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
We investigate practical algorithms for inconsistency-tolerant query answering over prioritized knowledge bases, which consist of a logical theory, a set of facts, and a priority relation between conflicting facts. We consider three…
This discussion paper re-examines SemEval-2020 Task 1, the most influential shared benchmark for lexical semantic change detection, through a three-part evaluative framework: operationalisation, data quality, and benchmark design. First, at…
First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…
Large Language Models (LLMs) are widely applied to downstream domains. However, current LLMs for high-stakes domain tasks, such as financial investment and legal QA, typically generate brief answers without reasoning processes and…
Optimizing an experimental system can be extremely challenging when each experiment is expensive, time-consuming, or difficult to perform. Existing optimizers for expensive black-box problems, such as Bayesian optimization, are typically…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may…
We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of…
Recent advancements in large language models have led to significant improvements across various tasks, including mathematical reasoning, which is used to assess models' intelligence in logical reasoning and problem-solving. Models are…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
Signal Temporal Logic (STL) is an expressive formal language for specifying spatio-temporal requirements over real-valued, real-time signals. It has been widely used for the verification and synthesis of autonomous systems and…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…