Aristotle’s Square Revisited to Frame Discovery Science

Afshar, Mohammad; Dartnell, Christopher; Luzeaux, Dominique; Sallantin, Jean; Tognetti, Yannick

doi:10.4304/jcp.2.5.54-66

Cited by 13 publications

(3 citation statements)

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“…There are many publications that are related to this area. Recall the work of Peterson [10] and many others (see [4,14]). In [9], the author presents classical and modern squares of opposition, where the problem with presupposition is discussed.…”

Section: Analysis Of the Generalized Square Of Oppositionmentioning

confidence: 99%

The analysis of the generalized square of opposition

Murinová¹,

Novák²

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In this paper, we continue the development of a formal theory of intermediate quantifiers (linguistic expressions such as "most", "many", "few", "almost all", etc.).In previous work, we demonstrated that 105 generalized syllogisms are valid in our theory. We turn our attention to another problem which is the analysis of the generalized Aristotelian square of opposition which, besides the classical quantifiers, is extended also by several selected intermediate quantifiers. We show that the expected relations can be well modeled in our theory. The formal theory of intermediate quantifiers is developed within a special higher-order fuzzy logic -Łukasiewicz fuzzy type theory.

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Section: Analysis Of the Generalized Square Of Oppositionmentioning

confidence: 99%

The analysis of the generalized square of opposition

Murinová¹,

Novák²

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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“…Induction has been studied from different angles, in particular by Pierce and Suppes, before the Inductive Logic Programming community suggested a more practical approach. Numerous investigations on automatic or semi-automatic scientific discovery have taken place [5,7,3,1]. Finally, let us mention the more recent work on the relationships between scientific discovery and game theory; but these pointers do not by far exhaust the whole body of work on the relationship between rationality and scientific discovery.…”

Section: Introductionmentioning

confidence: 99%

A Dialectic Approach to Problem-Solving

Martin

Sallantin

2009

Discovery Science

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We analyze the dynamics of problem-solving in a framework which captures two key features of that activity. The first feature is that problem-solving is a social game where a number of problem-solvers interact, rely on other agents to tackle parts of a problem, and regularly communicate the outcomes of their investigations. The second feature is that problem-solving requires a careful control over the set of hypotheses that might be needed at various stages of the investigation for the problem to be solved; more particularly, that any incorrect hypothesis be eventually refuted in the face of some evidence: all agents can expect such evidence to be brought to their knowledge whenever it holds. Our presentation uses a very general form of logic programs, viewed as sets of rules that can be activated and fire, depending on what a problem-solver is willing to explore, what a problem-solver is willing to hypothesize, and what a problem-solver knows about the problem to be solved in the form of data or background knowledge. Our framework supports two fundamental aspects of problem-solving. The first aspect is that no matter how the work is being distributed amongst agents, exactly the same knowledge is guaranteed to be discovered eventually. The second aspect is that any group of agents (with at one end, one agent being in charge of all rules and at another end, one agent being in charge of one and only one rule) might need to sometimes put forward some hypotheses to allow for the discovery of a particular piece of knowledge in finite time.

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“…Recall the work of Peterson [25] and many others (see [3]). In [22], the author presents classical and modern squares of opposition, where the problem with presupposition is discussed ¶) .…”

Section: Interpretation Of "Many"mentioning

confidence: 99%