Related papers: First-Order Logic in Finite Domains: Where Semanti…
Modern state-of-the-art Semantic Role Labeling (SRL) methods rely on expressive sentence encoders (e.g., multi-layer LSTMs) but tend to model only local (if any) interactions between individual argument labeling decisions. This contrasts…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
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…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for…
Evaluating large language models (LLMs) on natural-language logical reasoning is essential because rule-governed tasks require conclusions to follow strictly from stated premises. Many existing logical-reasoning benchmarks are generated by…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
We explore a kind of first-order predicate logic with intended semantics in the reals. Compared to other approaches in the literature, we work predominantly in the multiplicative reals $[0,\infty]$, showing they support three generations of…
We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…
Justification logic is a term used to identify a relatively new family of modal-like logics. There is an established literature about propositional justification logic, but incursions on the first-order case are scarce. In this paper we…
We present SemanticQA, an evaluation suite designed to assess language models (LMs) in semantic phrase processing tasks. The benchmark consolidates existing multiword expression (MwE) resources and reorganizes them into a unified testbed.…
Model semantics for first-order predicate logic is characterized by a visual inference tool called semantic forcing trees for predicate logic. Formulas that are valid (or invalid) by semantic forcing trees match valid (or invalid) formulas…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Artificial Intelligence problems, ranging form planning/scheduling up to game control, include an essential crucial step: describing a model which accurately defines the problem's required data, requirements, allowed transitions and…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
Model checking for real-timed systems is a rich and diverse topic. Among the different logics considered, Metric Interval Temporal Logic (MITL) is a powerful and commonly used logic, which can succinctly encode many interesting timed…
Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the…