Related papers: Argumentation in Mathematical Practice
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
The standard notion of formal theory, in Logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
Particularly in transgender and nonbinary (TGNB) communities, it is an increasingly common practice to publicly share one's personal pronouns so that we may be gendered correctly in others' speech. Many of us have nuanced desires for how we…
We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we…
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…
Artificial Intelligence (AI) is being increasingly used to develop systems that produce intelligent solutions. However, there is a major concern that whether the systems built will be trusted by humans. In order to establish trust in AI…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
We introduce matrix and its block to the Dung's theory of argumentation framework. It is showed that each argumentation framework has a matrix representation, and the indirect attack relation and indirect defence relation can be…
I analyse differences in style between traditional prose mathematics writing and computer-formalised mathematics writing, presenting five case studies. I note two aspects where good style seems to differ between the two: in their…
Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between…
I aim to promote an alternative agenda for teaching modal logic chiefly inspired by the relationships between modal logic and philosophy. The guiding idea for this proposal is a reappraisal of the interest of modal logic in philosophy,…
To resolve conflicts among norms, various nonmonotonic formalisms can be used to perform prioritized normative reasoning. Meanwhile, formal argumentation provides a way to represent nonmonotonic logics. In this paper, we propose a…
We propose the study of mathematical ludology, which aims to formally interrogate questions of interest to game studies and game design in particular. The goal is to extend our mathematical understanding of complex games beyond…
Despite the 'apparent clarity' of a given legal provision, its application may result in an outcome that does not exactly conform to the semantic level of a statute. The vagueness within a legal text is induced intentionally to accommodate…