Related papers: Discernment is all you need
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
Concept-based explanations have emerged as a popular way of extracting human-interpretable representations from deep discriminative models. At the same time, the disentanglement learning literature has focused on extracting similar…
Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose…
This study intends to systematically disentangle pure logic reasoning and text understanding by investigating the contrast across abstract and contextualized logical problems from a comprehensive set of domains. We explore whether LLMs…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by…
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…
We use language to communicate our thoughts. But is language merely the expression of thoughts, which are themselves produced by other, nonlinguistic parts of our minds? Or does language play a more transformative role in human cognition,…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic…
The Epistemic Halpern-Shoham logic (EHS) is a temporal-epistemic logic that combines the interval operators of the Halpern-Shoham logic with epistemic modalities. The semantics of EHS is based on interpreted systems whose labelling function…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The…