Related papers: Model-theoretic characterization of predicate intu…

We introduce a homotopy-theoretic interpretation of intuitionistic first-order logic based on ideas from Homotopy Type Theory. We provide a categorical formulation of this interpretation using the framework of Grothendieck fibrations. We…

First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…

We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order;…

Validation is a major challenge in differentiable programming. The state of the art is based on algorithmic differentiation. Consistency of first-order tangent and adjoint programs is defined by a well-known first-order differential…

The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…

Intuitionistic dependence logic was introduced by Abramsky and Vaananen (2009) as a variant of dependence logic under a general construction of Hodges' (trump) team semantics. It was proven that there is a translation from intuitionistic…

In this paper, we propose a first-order ontology for generalized stratified order structure. We then classify the models of the theory using model-theoretic techniques. An ontology mapping from this ontology to the core theory of Process…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

A cyclic proof system gives us another way of representing inductive definitions and efficient proof search. In 2011 Brotherston and Simpson conjectured the equivalence between the provability of the classical cyclic proof system and that…

Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive…

We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…

This paper examines the application of Tarski's Undefinability Theorem to first-order arithmetic. The generally accepted view is that for this case the Theorem establishes that arithmetic truth is not arithmetic. A careful examination of…

First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…

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…

We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as preorders. The logic is equipped with a precise syntactic…

In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…

A logic satisfies the interpolation property provided that whenever a formula {\Delta} is a consequence of another formula {\Gamma}, then this is witnessed by a formula {\Theta} which only refers to the language common to {\Gamma} and…

First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…