Related papers: First-Order Stable Model Semantics and First-Order…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
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…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Modern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are implemented to tackle highly irregular problems where…
We study the following problem: given a class of logic programs C, determine the maximum number of stable models of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of…
A propositional logic program $P$ may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, describes…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model,…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from…
In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by…
We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments…
We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…
A seminal result of Kamp is that over the reals Linear Temporal Logic (LTL) has the same expressive power as first-order logic with binary order relation < and monadic predicates. A key question is whether there exists an analogue of Kamp's…
This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a…