extensionality


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extensionality

(ɪkˌstɛnʃəˈnælɪtɪ)
n
(Logic) logic the principle that sets are definable in terms of their elements alone, whatever way they may have been selected. Thus {a, b}={b, a}={first two letters of the alphabet}
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This paper argues that these two distinct conceptions have been conflated to date, citing the puzzles of overdetermination, extensionality, and transitivity as evidence.
What could be done as a way of indicating that A has a higher Allness Index or lower Extensionality Index than B?
There is, manifestly, a case to be made here for the extensionality of emotions, which Griffero's framework can both enrich and develop.
Suppositional, extensionality and conditionals: a critique of the Mental Model Theory of Johnson-Laird and Byrne (2002).
We may have no better choice in considering the full range of Quine-inspired substitution failures, entirely outside of modal context applications and the problem of quantifying into supposedly "intensional" modal contexts, assuming the extensionality of identity and the reflexivity of identity applied to propositions as objects.
According to Table 8, this PSO-RBFNN has a good fitness capability and extensionality. The fitness error and prediction error are illustrated in Figure 9.
Chapter 2 covers many-valued and modal logics, with algebraic semantics; Chapter 3 is about properties of connectives such as truth-functionality and extensionality. The last preliminary chapter, Chapter 4, is concerned mainly with the existence and uniqueness of the connectives.
In the axiomatic reconstruction (Kalinowski 1972: 84-85) of the "old system" (the first version of deontic logic, dating from 1951), we will find four "principles" (von Wright 1951): extensionality (PE): PA [left and right arrow] PB if A and B are actions of the same agent and have the same value of achievement; (unilateral) permission distribution (PPD): P(A [disjunction] B) [left and right arrow] (PA [disjunction] PB); permission (PP): PA [disjunction] P([logical not] A); tautology (PT): -P(A & [logical not] A); we also find the principle of deontic contingence: "a tautological act is not necessarily obligatory and an obligatory act is not necessarily forbidden".
Six axiom schemes define the basic operators and the extensionality which, in turn, defines the equality of two sets.
The term "intensional" means that they violate the principle of extensionality, the principle that extensional equivalence implies identity.
For logics of agency, extensionality is often not realistic.
What is still missing is extensionality, in the Leibnizian sense of extension in contrast to intension, the former pointing beyond the expression to aboutness and reference, the latter to the mode in which the extension is presented, its definitional coherence or, in Husserlian parlance, perhaps its 'noematic nucleus'.