Abstract logic of oppositions

Schang, Fabien

doi:10.12775/llp.2012.019

Cited by 3 publications

(2 citation statements)

References 10 publications

(13 reference statements)

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“…In the third part of the paper, the logical octagon was explored syntactically and semantically with the modern methods of first-order logic and model theory. The final result and expectedly unprecedented contribution 9 is a bitstring semantics (see Schang 2012Schang , 2018, which completes the account offered by Demey and Smessaert 2018 in syntactic terms of duality and literally 'shows' the truth-conditions of categorical propositions in terms of ordered model sets every proposition belongs to or not. By this way, we hope to get two main results: a clarification of the logical octagon by means of its formal reconstruction; a generalization of the theory of oppositions, from the initial dependence to the final independence relations between any well-formed formulas.…”

Section: Discussionsupporting

confidence: 59%

Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions

Moktefi

Schang

2023

History and Philosophy of Logic

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The aim of this paper is to make sense of the Keynes-Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.

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Section: Discussionsupporting

confidence: 59%

Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions

Moktefi

Schang

2023

History and Philosophy of Logic

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“…An algebraic proof of the above logical relations can be given in Boolean terms, following some previous results (see [9,14]). In a nutshell, logical opposition are to be defined by set-theoretical operations of meet and join on bitstrings.…”

Section: Fuzzy Questionsmentioning

confidence: 88%

The Logical Burdens of Proof. Assertion and Hypothesis

Chiffi

Schang

2017

LLP

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Abstract. The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR4 and AR 4 , respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding to a wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics.

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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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Abstract logic of oppositions

Cited by 3 publications

References 10 publications

Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions

Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions

The Logical Burdens of Proof. Assertion and Hypothesis

Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

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