On Tarski's formalization of predicate logic with identity

Kalish, Donald; Montague, Richard

doi:10.1007/bf01969434

Cited by 35 publications

(30 citation statements)

References 4 publications

(15 reference statements)

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“…The motivation is analogous to that of the preceding papers of Tarski [14] and of Kalish and Montague [11]. The motivation is analogous to that of the preceding papers of Tarski [14] and of Kalish and Montague [11].…”

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confidence: 82%

“…Moreover, Montague has observed that A" has the following properties, and that this can be shown by essentially the same methods which were used in [11] to show that Z~ has analogous properties: (1) if = A a T e US n FMS, thenA" w { ~ A a ~} is complete, i.e., A~') be the set of all closures of sentences ofA (resp.…”

Section: H Q~ ~ Fms and A R Fv (Q) Then Al ~ Q -+ A A Qmentioning

confidence: 95%

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Substitutionless predicate logic with identity

Monk

1965

Arch math Logik

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I n t r o d u c t i o n. The main object of this paper is to simplify the usual framework for predicate logic (with identity). The motivation is analogous to that of the preceding papers of Tarski [14] and of Kalish and Montague [11]. In those papers, working with the ordinary rules of formula formation, the authors give very simple axiom systems for the universally valid formulas and sentences of predicate logic. Thus in describing the axioms of system ~ of [14] only two notions of any degree of complexity at all appear: the notion of the set of variables occurring in a formula, and the notion of substituting one variable for another in an atomic formula. By modifying the formation rules of predicate logic we will be able to eliminate this last notion.The modification consists in having after each non-logical predicate a fixed string of variables depending upon the particular predicate but not changing for different occurrences of the same predicate. Identity is considered as a logical notion, and so full substitution is allowed in atomic identity formulas. The possibility of still obtaining an adequate system of predicate logic using this formation rule may be illustrated by the following example. In ordinary logic, let ~ be a binary predicate. Then the formula

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confidence: 82%

Section: H Q~ ~ Fms and A R Fv (Q) Then Al ~ Q -+ A A Qmentioning

confidence: 95%

Substitutionless predicate logic with identity

Monk

1965

Arch math Logik

View full text Add to dashboard Cite

show abstract

“…[7], [8]. We restrict ourselves in this paper to systems of predicate logic in which predicates (relation symbols) occur as the only non-logical constants.…”

Section: Alfred Tarekimentioning

confidence: 99%

“…Given any two formulas r and ~v, we shall denote, as usual, (A9'") [a ~ 8 --> (r ~ a --> ~ ~ 8)]" The relation of these schemata to (A8) and (A9) of the system ~1 is clear. Assume first for simplicity that we are interested in predicate logic in which a binary predicate g occurs as the only non-logical constant.…”

Section: ~ a Ao~ H An-~ ~ --> A A~o H A~~_~ ~mentioning

confidence: 99%