For example, in the language of rings, there are constant symbols 0 and 1, two binary function symbols + and ? and no binary relation symbols . ( Here the equality relation is taken as a logical constant .)
12.
This impredicative theory generalized predicative type theory as presented in his 1984 Bibliopolis book, and extended in a number of increasingly philosophical texts, such as his influential " On the Meanings of the Logical Constants and the Justifications of the Logical Laws ".
13.
Note that all our interpretation does is assign the extension { a } to the non-logical constant " T ", and does not make a claim about whether " T " is to stand for tall and'a'for Abraham Lincoln.
14.
Prior to 1927 Boolean algebra had been considered a calculus of logical values with logical operations of conjunction, disjunction, negation, etc . Zhegalkin showed that all Boolean operations could be written as ordinary numeric polynomials, thinking of the logical constants 0 and 1 as integers mod 2.
15.
According to [ Ferraris, 2005 ], the " reduct " of a propositional formula F relative to a set I of atoms is the formula obtained from F by replacing each maximal subformula that is not satisfied by I with the logical constant \ bot ( false ).
16.
A model in the empirical sciences is an " intended factually-true descriptive interpretation " ( or in other contexts : a non-intended arbitrary interpretation used to clarify such an intended factually-true descriptive interpretation . ) All models are interpretations that have the same domain of discourse as the intended one, but other assignments for non-logical constants.
17.
Lenk started out with the philosophy of science and the foundation of logics ( notably his habilitation thesis on the Critique of Logical Constants, 1968 ) and later on, since 1978, included epistemology and pragmatic methodology of the social and natural sciences, technology + economics, neuroscience and the philosophy of language in several books on Interpretative Constructs ( 1993 ) and Schema Games ( 1995 ).
18.
"Logical pluralism " can be defined a number of ways : the position that there is more than one correct account of logical consequence ( or no single,'correct'account at all ), that there is more than once correct set of logical constants or even that the'correct'logic depends on the relevant logical questions under consideration ( a sort of logical instrumentalism ).
19.
Previous logic had dealt with the logical constants " and ", " or ", " if . . . then . . . ", " not ", and " some " and " all ", but iterations of these operations, especially " some " and " all ", were little understood : even the distinction between a sentence like " every boy loves some girl " and " some girl is loved by every boy " could be represented only very artificially, whereas Frege's formalism had no difficulty expressing the different readings of " every boy loves some girl who loves some boy who loves some girl " and similar sentences, in complete parallel with his treatment of, say, " every boy is foolish ".
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