Predicative Arithmetic
Predicative may refer to: * Something having the properties of a grammatical predicate ** Predicative expression, part of a clause that typically follows a copula (linking verb) ** Predicative verb, a verb that behaves as a grammatical adjective * In mathematics and logic something without impredicativity, without a self-referencing definition * Predicative programming Predicative programming is the original name of a formal method for program specification and refinement, more recently called a Practical Theory of Programming, invented by Eric Hehner. The central idea is that each specification is a binary (bool ...

Grammatical Predicate
The term predicate is used in one of two ways in linguistics and its subfields. The first defines a predicate as everything in a standard declarative sentence except the subject, and the other views it as just the main content verb or associated predicative expression of a clause. Thus, by the first definition the predicate of the sentence ''Frank likes cake'' is ''likes cake''. By the second definition, the predicate of the same sentence is just the content verb ''likes'', whereby ''Frank'' and ''cake'' are the arguments of this predicate. Differences between these two definitions can lead to confusion. Syntax Traditional grammar The notion of a predicate in traditional grammar traces back to Aristotelian logic. A predicate is seen as a property that a subject has or is characterized by. A predicate is therefore an expression that can be ''true of'' something. Thus, the expression "is moving" is true of anything that is moving. This classical understanding of predicates wa ...
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Predicative Expression
A predicative expression (or just predicative) is part of a clause predicate, and is an expression that typically follows a copula (or linking verb), e.g. ''be'', ''seem'', ''appear'', or that appears as a second complement of a certain type of verb, e.g. ''call'', ''make'', ''name'', etc. The most frequently acknowledged types of predicative expressions are predicative adjectives (also ''predicate adjectives'') and predicative nominals (also ''predicate nominals''). The main trait of all predicative expressions is that they serve to express a property that is assigned to a "subject", whereby this subject is usually the clause subject, but at times it can be the clause object. A primary distinction is drawn between predicative (also ''predicate'') and attributive expressions. Further, predicative expressions are typically ''not'' clause arguments, and they are also typically ''not'' clause adjuncts. There is hence a three-way distinction between predicative expressions, argum ...
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Predicative Verb
A predicative verb is a verb that behaves as a grammatical adjective; that is, it predicates (qualifies or informs about the properties of its argument). It is a special kind of stative verb. Many languages do not use the present forms of the verb "to be" to separate an adjective from its noun: instead, these forms of the verb "to be" are understood as part of the adjective. Egyptian uses this structure: "my mouth is red" is written as "red my mouth" (/dSr=f r=i/). Other languages to use this structure include the Northwest Caucasian languages, the Thai language, Indonesian, the East Slavic languages, the Semitic languages, some Nilotic languages and the Athabaskan languages. Many adjectives in Chinese and Japanese also behave like this. In the Akkadian language Akkadian (, Akkadian: )John Huehnergard & Christopher Woods, "Akkadian and Eblaite", ''The Cambridge Encyclopedia of the World's Ancient Languages''. Ed. Roger D. Woodard (2004, Cambridge) Pages 218-280 is an e ...
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Impredicativity
In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative. Authors have given different but related definitions. The opposite of impredicativity is predicativity, which essentially entails building stratified (or ramified) theories where quantification over lower levels results in variables of some new type, distinguished from the lower types that the variable ranges over. A prototypical example is intuitionistic type theory, which retains ramification so as to discard impredicativity. Russell's paradox is a famous example of an impredicative construction—namely the set of all sets that do not contain themselves. The paradox is that ...
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