Aristotelian Diagrams in the Debate on Future Contingents

Demey, Lorenz

doi:10.1007/s11841-017-0632-7

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…The octagon in Figure 2(b) was already studied by the 14th-century philosopher John Buridan [31,52,55,76]. This clearly illustrates the fact that Aristotelian diagrams have a long and rich history in philosophy [20,21,67]. However, today they are also widely used in other areas, including artificial intelligence.…”

Section: Introductionmentioning

confidence: 89%

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Geometric and cognitive differences between logical diagrams for the Boolean algebra B 4 $\mathbb {B}_{4}$

Demey

Smessaert

2018

Ann Math Artif Intell

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Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B 4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams (such as the rhombic dodecahedron) and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design principles such as congruence/isomorphism and apprehension. The cognitive effectiveness of the different visualizations is compared for the representation of implication versus opposition relations, and for subdiagram embeddings.

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Section: Introductionmentioning

confidence: 89%

“…For example, we have dRDH (1000, 1110) = 2 < 2.83 = dRDH (1000, 0001), and yet dH (1000, 1110) = 2 = dH (1000, 0001) 21. For example, we have dNTH (1000, 1100) = 1.41 < 2.45 = dNTH (1000, 0110) and also dH (1000, 1100) = 1 < 3 = dH (1000, 0110) 22.…”

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confidence: 99%

Geometric and cognitive differences between logical diagrams for the Boolean algebra B 4 $\mathbb {B}_{4}$

Demey

Smessaert

2018

Ann Math Artif Intell

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“…For example, Yao (2013), Ciucci et al (2014Ciucci et al ( , 2016 and Dubois et al (2015) have pointed out the heuristic usefulness of Aristotelian diagrams in the theoretical foundations of artificial intelligence, emphasizing their role in drawing comparisons across individual knowledge representation formalisms and in discovering new notions (by transferring them across formalisms). Demey (2017bDemey ( , 2018aDemey ( , 2018c and Demey and Smessaert (2018) generalize these remarks to the applicability of Aristotelian diagrams in (drawing comparisons between) other areas, such as Russell's theory of definite descriptions and public announcement logic.…”

Section: Introductionmentioning

confidence: 91%

Aristotelian diagrams for semantic and syntactic consequence

Demey

2018

Synthese

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Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the wellknown square of opposition for the categorical statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system's soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation. has been a surge of interest in Aristotelian diagrams at the metalogical level, which contain statements or notions belonging to the metatheory of a given logical system. For example,

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“…The technique of bitstring semantics was initially developed within the specific context of logical geometry [38], but in recent years it has started to find applications across the disciplines of logic [9,15,16,27], philosophy [10,11,23] and linguistics [34,39]. In general, bitstring semantics allows us to systematically compute combinatorial representations of a given number of propositions, thus providing a concrete grip on their logical behavior.…”

Section: Bitstring Semanticsmentioning

confidence: 99%

Logic-Sensitivity and Bitstring Semantics in the Square of Opposition

Demey,

Frijters

2023

J Philos Logic

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This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term 'bitstring semantics'!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective.

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Aristotelian Diagrams in the Debate on Future Contingents

Cited by 6 publications

References 15 publications

Geometric and cognitive differences between logical diagrams for the Boolean algebra B 4 $\mathbb {B}_{4}$

Geometric and cognitive differences between logical diagrams for the Boolean algebra B 4 $\mathbb {B}_{4}$

Aristotelian diagrams for semantic and syntactic consequence

Logic-Sensitivity and Bitstring Semantics in the Square of Opposition

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