Related papers: A First-Order Logic with Frames

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

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…

This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given…

First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…

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 a logical framework for the verification of relational properties in imperative programs. Our work is motivated by relational properties which come from security applications and often require reasoning about formulas with…

The logic of information flows (LIF) has recently been proposed as a general framework in the field of knowledge representation. In this framework, tasks of procedural nature can still be modeled in a declarative, logic-based fashion. 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…

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…

We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a…

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…

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…

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…

This paper presents a method for inducing logic programs from examples that learns a new class of concepts called first-order decision lists, defined as ordered lists of clauses each ending in a cut. The method, called FOIDL, is based on…

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…

In this paper, we study the sampling problem for first-order logic proposed recently by Wang et al. -- how to efficiently sample a model of a given first-order sentence on a finite domain? We extend their result for the…

Translating formal language into natural language is a foundational challenge in NLP, driving various downstream applications in semantic parsing, theorem validation, and question answering. In this study, we introduce First-Order Logic to…

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…