Related papers: Towards a Logic for Reasoning About LF Specificati…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
The profusion of knowledge encoded in large language models (LLMs) and their ability to apply this knowledge zero-shot in a range of settings makes them promising candidates for use in decision-making. However, they are currently limited by…
Formal specifications play a pivotal role in accurately characterizing program behaviors and ensuring software correctness. In recent years, leveraging large language models (LLMs) for the automatic generation of program specifications has…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
This paper introduces an explanation framework designed to enhance the quality of rules in knowledge-based reasoning systems based on dataset-driven insights. The traditional method for rule induction from data typically requires…
Although LLMs have shown great performance on Mathematics and Coding related reasoning tasks, the reasoning capabilities of LLMs regarding other forms of reasoning are still an open problem. Here, we examine the issue of reasoning from the…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
We extend the formal framework of classifier models used in the legal domain. While the existing classifier framework characterises cases solely through the facts involved, legal reasoning fundamentally relies on both facts and rules,…
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…
Dedukti is a very expressive logical framework which unlike most frameworks, such as the Edinburgh Logical Framework (LF), allows for the representation of computation alongside deduction. However, unlike LF encodings, Dedukti encodings…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
First Order Logic (FOL) is a powerful reasoning tool for program verification. Recent work on Ivy shows that FOL is well suited for verification of parameterized distributed systems. However, specifying many natural objects, such as a ring…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…
LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF.…