Related papers: First-Order Logic in Finite Domains: Where Semanti…
Sentential Calculus with Identity (SCI) is an extension of classical propositional logic, featuring a new connective of identity between formulas. In SCI two formulas are said to be identical if they share the same denotation. In the…
Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
Semantic similarity measures (SSMs) are widely used in biomedical research but remain underutilized in pharmacovigilance. This study evaluates six ontology-based SSMs for clustering MedDRA Preferred Terms (PTs) in drug safety data. Using…
Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
We present SENTINEL, a framework for formally evaluating the physical safety of foundation model (FM)-based embodied agents. SENTINEL is the first to provide multi-level safety evaluation across semantic interpretation, plan generation, and…
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…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
We present a novel length-aware solving algorithm for the quantifier-free first-order theory over regex membership predicate and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3…
A novel first-order equivalent static loads approach for optimization of structural dynamic response, F-ESL, is presented and compared to the basic equivalent static load formulation, ESL. F-ESL simplifies dynamic optimization problems by…
In recent years, the surge in unstructured data analysis, facilitated by advancements in Machine Learning (ML), has prompted diverse approaches for handling images, text documents, and videos. Analysts, leveraging ML models, can extract…
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…
Translating natural language into formal language such as First-Order Logic (FOL) is a foundational challenge in NLP with wide-ranging applications in automated reasoning, misinformation tracking, and knowledge validation. In this paper, we…
Recent years have witnessed a wide array of results in software testing, exploring different approaches and methodologies ranging from fuzzers to symbolic engines, with a full spectrum of instances in between such as concolic execution and…
In quantum information and computation research, symbolic methods have been widely used for human specification and reasoning about quantum states and operations. At the same time, they are essential for ensuring the scalability and…
Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…
The Shapes Constraint Language (SHACL) is a recent W3C recommendation language for validating RDF data. Specifically, SHACL documents are collections of constraints that enforce particular shapes on an RDF graph. Previous work on the topic…
We address the problem of semantic querying of relational databases (RDB) modulo knowledge bases using very expressive knowledge representation formalisms, such as full first-order logic or its various fragments. We propose to use a…
Recent alignment studies commonly remove introductory boilerplate phrases from supervised fine-tuning (SFT) datasets. This work challenges that assumption. We hypothesize that safety- and reasoning-oriented prefix sentences serve as…