Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation

Pease, Alison; Lawrence, John; Budzyńska, Katarzyna; Corneli, Joseph; Reed, Chris

doi:10.1016/j.artint.2017.02.006

Cited by 20 publications

(25 citation statements)

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“…Pease et al (2017) show how AI techniques for understanding abstract argumentation and its connections to structured argumentation, linguistic expression of reasoning and dialogical practice can work together in a complete cycle, from real-world argument to philosophical account, formal theory, abstract argumentation and argumentation semantics, and back to application to real-world argument. Extending earlier work (Pease et al 2014), we describe each stage in the cycle both formally and our implementation of it, employing a range of argument tools described above.…”

Section: Argument Miningmentioning

confidence: 99%

The Argument Web: an Online Ecosystem of Tools, Systems and Services for Argumentation

et al. 2017

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The Argument Web is maturing as both a platform built upon a synthesis of many contemporary theories of argumentation in philosophy and also as an ecosystem in which various applications and application components are contributed by different research groups around the world. It already hosts the largest publicly accessible corpora of argumentation and has the largest number of interoperable and cross compatible tools for the analysis, navigation and evaluation of arguments across a broad range of domains, languages and activity types. Such interoperability is key in allowing innovative combinations of tool and data reuse that can further catalyse the development of the field of computational argumentation. The aim of this paper is to summarise the key foundations, the recent advances and the goals of the Argument Web, with a particular focus on demonstrating the relevance to, and roots in, philosophical argumentation theory.

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Section: Argument Miningmentioning

confidence: 99%

The Argument Web: an Online Ecosystem of Tools, Systems and Services for Argumentation

et al. 2017

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“…Lakatos's theory is limited, first, in its theoretical commitments, insofar as Lakatos's mathematics is closely linked to the Hegelian notion of thesis/antithesis/synthesis [42]. Secondly, even though Lakatos's theory is now implemented computationally (per [53]), the model leaves out concrete details of mathematical objects and relationships among them. The trace of a Lakatos Game does include content -but the relationships between elements are mediated by a controlled vocabulary of 20 dialog moves, whose sequence is structured into a game tree.…”

Section: Lakatos Gamesmentioning

confidence: 99%

“…Lakatos [37] developed an abstract, dialectical, model of mathematical creativity which has recently been formalized as one such dialogue game [52,53]. In the "Lakatos Game", assertions are made and then progressively refined through discussion and debate.…”

Section: Lakatos Gamesmentioning

confidence: 99%

“…We are not aware of any other representation framework that is both flexible and expressive enough to connect the formal and informal reasoning that is present in mainstream mathematical texts and dialogues. Our survey in §3 will point to structured proofs [40] and Lakatos Games [53] as two pieces of exemplary work that do not possess this bridging property. We also draw on Conceptual Dependence theory [45,61,64], and broadly, on a reflexive strategy for representation, because we are not only aiming to represent reasoning, but also to simulate it computationally -whereas IATC by itself is purely about representation.…”

Section: Introductionmentioning

confidence: 99%

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Modelling the way mathematics is actually done

Corneli

Martin

Murray-Rust

et al. 2017

Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design

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Whereas formal mathematical theories are well studied, computers cannot yet adequately represent and reason about mathematical dialogues and other informal texts. To address this gap, we have developed a representation and reasoning strategy that draws on contemporary argumentation theory and classic AI techniques for representing and querying narratives and dialogues. In order to make the structures that these modelling tools produce accessible to computational reasoning, we encode representations in a higherorder nested semantic network. This system, for which we have developed a preliminary prototype in LISP, can represent both the content of what people say, and the dynamic reasoning steps that move from one step to the next. CCS Concepts• Computing methodologies → Philosophical/theoretical foundations of artificial intelligence;

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“…Using this standardised format facilitates the comparison to other dialogue systems, such as Walton's CB [54], the Mediation Dialogue Game [16], or Lakatos' dialogical approach to mathematical proof [29]. Another advantage, shown by Wells and Reed [57], is the avoidance of the under-specification of the dialogue rules that can occur in non-computationally-implemented formal descriptions of dialogue games.…”

mentioning

confidence: 99%

A Critical Discussion Game for Prohibiting Fallacies

Visser

Budzyńska

Reed

2017

LLP

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Abstract. The study of fallacies is at the heart of argumentation studies. In response to Hamblin's devastating critique of the state of the theory of fallacies in 1970, both formal dialectical and informal approaches to fallacies developed. In the current paper, we focus on an influential informal approach to fallacies, part of the pragma-dialectical theory of argumentation. Central to the pragma-dialectical method for analysing and evaluating argumentative discourse is the ideal model of a critical discussion. In this discussion model, a dialectical perspective on argumentation is combined with a pragmatic take on communicative interaction. By formalising and computationally implementing the model of a critical discussion, we take a first step in the development of software to computationally model argumentative dialogue in which fallacies are prohibited along the pragmadialectical norms. We do this by defining the Critical Discussion Game, a formal dialogue game based on the pragma-dialectical discussion model, executable on an online user-interface which is part of a larger infrastructure of argumentation software.

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Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation

Cited by 20 publications

References 80 publications

The Argument Web: an Online Ecosystem of Tools, Systems and Services for Argumentation

The Argument Web: an Online Ecosystem of Tools, Systems and Services for Argumentation

Modelling the way mathematics is actually done

A Critical Discussion Game for Prohibiting Fallacies

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