Logical Oppositions in Arabic Logic: Avicenna and Averroes

Chatti, Saloua

doi:10.1007/978-3-0348-0379-3_2

Cited by 11 publications

(4 citation statements)

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“…Bitstrings provide a compact way of representing the semantics of the formulas in a given logical fragment or lexical field, and allow us to study the logical relations holding between these formulas in terms of their bitstring representations. 2 Although an informal precursor of this technique was already used by Avicenna in the 11th century AD (Chatti, 2012(Chatti, , 2014, its formal development began only in the last decade, inspired by considerations from generalized quantifier theory about partitioning the powerset of the quantificational domain (Smessaert, 2009). It has since been fruitfully applied to logical systems such as propositional logic, first-order logic and modal logic (Luzeaux et al, 2008;Smessaert, 2009;Smessaert and Demey, 2015c), and to lexical fields such as color terms, singular expressions and subjective quantification (Jaspers, 2012;Smessaert, 2012;Smessaert and Demey, 2015b).…”

Section: Logical Preliminariesmentioning

confidence: 99%

Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

Demey

Smessaert

2017

J Philos Logic

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Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before. Keywords bitstrings • combinatorial semantics • Aristotelian diagram • Boolean algebra • existential import • public announcement logic

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Section: Logical Preliminariesmentioning

confidence: 99%

Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

Demey

Smessaert

2017

J Philos Logic

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“…some but not all ). 15 The precise linguistic-cognitive details of this explanation need not concern us here, but given the striking analogy between all /some 1 /some 2 and CD/C w /C s , it should not be surprising if a broadly similar account also applies to the latter.…”

Section: Aristotelian Hexagons For Strong and Weak (Sub)contrarietymentioning

confidence: 99%

“…The key insight in studying this interaction is that strong contrariety and strong subcontrariety are themselves contrary 14 Completely analogously, one can of course also construct a strong JSB hexagon for strong/weak subcontrariety instead of strong/weak contrariety; see Figure 9(b). 15 The distinction between unilateral and bilateral interpretations can also be made for other quantifiers, such as many and few [80, p. 484ff.…”

Section: An Aristotelian Octagon For Strong and Weak (Sub)contrarietymentioning

confidence: 99%

“…It has a very rich tradition, going back-together with the discipline of logic itself-to the works of Aristotle. Over the centuries, authors such as Avicenna, William of Sherwood, John Buridan, Boole and Frege have studied the square and other, larger Aristotelian diagrams [15,16,40,48,63,67]. Since the beginning of the 21st century, logicians have started studying Aristotelian diagrams Parts of this paper were presented at CLMPS 15 (Helsinki).…”

Section: Introductionmentioning

confidence: 99%

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Metalogical Decorations of Logical Diagrams

Demey

Smessaert

2016

Log. Univers.

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Abstract. In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of (sub)contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object-and metalogical diagrams. Overall, the paper studies two types of logical diagrams (viz. Aristotelian and duality diagrams) and four kinds of metalogical decorations (viz. those based on the opposition, implication, Aristotelian and duality relations).Mathematics Subject Classification (2010). Primary 03A10, 03B45; Secondary 03B65, 03B80.

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Categorical Logic

Chatti¹

2019

Studies in Universal Logic

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Logical Oppositions in Arabic Logic: Avicenna and Averroes

Cited by 11 publications

References 5 publications

Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

Metalogical Decorations of Logical Diagrams

Categorical Logic

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