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This paper presents a general framework about what is a decision problem. Our motivation is related to the fact that decision analysis and operational research are structured (as disciplines) around classes of methods, while instead we…

Artificial Intelligence · Computer Science 2023-01-10 Alberto Colorni , Alexis Tsoukiàs

Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…

Artificial Intelligence · Computer Science 2015-04-21 Ryuta Arisaka

Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…

History and Overview · Mathematics 2019-04-25 Tiziana Castellano , Pietro Boccadoro

The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…

Logic in Computer Science · Computer Science 2017-02-16 Marc Denecker , Bart Bogaerts , Joost Vennekens

For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…

Logic · Mathematics 2013-12-17 Jesse Alama

Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which…

Logic in Computer Science · Computer Science 2025-07-22 Paolo Liberatore

Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…

Artificial Intelligence · Computer Science 2007-05-23 Daniel Lehmann

This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in…

History and Overview · Mathematics 2013-10-08 Charlotte Werndl

Can artificial intelligence discover, from raw experience and without human supervision, concepts that humans have discovered? One challenge is that human concepts themselves are fluid: conceptual boundaries can shift, split, and merge as…

Artificial Intelligence · Computer Science 2025-12-24 Zhengmian Hu

Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…

Computation and Language · Computer Science 2009-10-09 Alain Lecomte , Myriam Quatrini

A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…

Disordered Systems and Neural Networks · Physics 2007-05-23 Joao Martins , R. Vilela Mendes

We consider emergence from the perspective of dynamics: states of a system evolving with time. We focus on the role of a decomposition of wholes into parts, and attempt to characterize relationships between levels without reference to…

History and Philosophy of Physics · Physics 2024-10-22 Sean M. Carroll , Achyuth Parola

It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…

Logic in Computer Science · Computer Science 2007-07-10 Frédéric Blanqui , Jean-Pierre Jouannaud , Pierre-Yves Strub

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

Logic in Computer Science · Computer Science 2018-10-18 Andrea Condoluci , Matteo Manighetti

Is it true that if citizens understand hurricane probabilities, they will make more rational decisions for evacuation? Finding answers to such questions is not straightforward in the literature because the terms judgment and decision making…

Human-Computer Interaction · Computer Science 2024-10-18 Başak Oral , Pierre Dragicevic , Alexandru Telea , Evanthia Dimara

The research of attribute characters in information system which contains core, necessary, unnecessary is a basic and important issue in attribute reduct. Many methods for the judgement of attribute characters are based on the relationship…

Data Structures and Algorithms · Computer Science 2015-03-13 Anhui Tan

There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…

Artificial Intelligence · Computer Science 2014-04-25 Ryuta Arisaka

The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure…

History and Philosophy of Physics · Physics 2019-11-22 Erik Curiel

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…

Logic · Mathematics 2010-10-05 K. Dosen , Z. Petric

Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…

Artificial Intelligence · Computer Science 2026-04-03 Yiling Wu