Related papers: Reasoning by Analogy in Mathematical Practice
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
LLMs face significant challenges in systematic generalization, particularly when dealing with reasoning tasks requiring compositional rules and handling out-of-distribution examples. To address these challenges, we introduce an in-context…
This paper revisits the foundations of mathematical proof through the lens of Aristotle's threefold conception of truth: sensory evidence, axiomatic definition, and syllogistic deduction. I argue that modern mathematics has too often…
Fact-checking the truthfulness of claims usually requires reasoning over multiple evidence sentences. Oftentimes, evidence sentences may not be always self-contained, and may require additional contexts and references from elsewhere to…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves {stochastic mathematical systems} (SMSs), which are stochastic processes that generate pairs of questions and…
Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…
Presupposition projection in conditionals is central to theories of meaning and pragmatics, yet it remains largely unevaluated in large language models. We address this gap through a parallel behavioral study comparing human judgments and…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…
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…
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…