Related papers: Inductive Reasoning with Equality Predicates, Cont…
We define a class of formal systems inspired by Prawitz's theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to…
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…
Active inference is a leading theory of perception, learning and decision making, which can be applied to neuroscience, robotics, psychology, and machine learning. Active inference is based on the expected free energy, which is mostly…
Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Reasoning is an important task for large language models (LLMs). Among all the reasoning paradigms, inductive reasoning is one of the fundamental types, which is characterized by its particular-to-general thinking process and the…
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate…
Abductive reasoning aims to find plausible explanations for an event. This style of reasoning is critical for commonsense tasks where there are often multiple plausible explanations. Existing approaches for abductive reasoning in natural…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…