Related papers: INDUCTION: Finite-Structure Concept Synthesis in F…

We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…

In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…

We introduce in this work a novel stochastic inference process, for scene annotation and object class segmentation, based on finite state machines (FSMs). The design principle of our framework is generative and based on building, for a…

Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…

There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…

Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…

A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…

Conventional spoken language understanding systems consist of two main components: an automatic speech recognition module that converts audio to a transcript, and a natural language understanding module that transforms the resulting text…

Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the…

We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…

Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…

Recent large language models achieve strong reasoning performance by generating detailed chain-of-thought traces, but this often leads to excessive token use and high inference latency. Existing efficiency approaches typically focus on…

Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…

Early Exiting is one of the most popular methods to achieve efficient inference. Current early exiting methods adopt the (weighted) sum of the cross entropy loss of all internal classifiers during training, imposing all these classifiers to…

One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…

Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…

Strong inductive biases enable learning from little data and help generalization outside of the training distribution. Popular neural architectures such as Transformers lack strong structural inductive biases for seq2seq NLP tasks on their…

We present an approach to automatically synthesise recursive predicates in Separation Logic (SL) from concrete data structure instances using Inductive Logic Programming (ILP) techniques. The main challenges to make such synthesis effective…

As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…

Recent pre-trained language models (PLMs) equipped with foundation reasoning skills have shown remarkable performance on downstream complex tasks. However, the significant structure reasoning skill has been rarely studied, which involves…