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The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything true in all models is provable".
A sentence diagram is a pictorial representation of the grammatical structure of a sentence. The term "sentence diagram" is used more when teaching written language, where sentences are diagrammed. The model shows the relations between words and the nature of sentence structure and can be used as a tool to help recognize which potential ...
Two illustrations of the manner in which constituency tests deliver clues about constituent structure and thus about the correct ICA of a given sentence are now given. Consider the phrase The girl in the following trees: The acronym BPS stands for "bare phrase structure", which is an indication that the words are used as the node labels in the ...
Consistent sentence: A sentence of is consistent if it is true under at least one interpretation. It is inconsistent if it is not consistent. [ 66 ] [ 68 ] An inconsistent formula is also called self-contradictory , [ 1 ] and said to be a self-contradiction , [ 1 ] or simply a contradiction , [ 81 ] [ 82 ] [ 83 ] although this latter name is ...
The computational complexity of determining whether a given sentence has probability tending to zero or to one is high: the problem is PSPACE-complete. [9] If a first-order graph property has probability tending to one on random graphs, then it is possible to list all the n {\displaystyle n} -vertex graphs that model the property, with ...
The Penrose–Lucas argument is a logical argument partially based on a theory developed by mathematician and logician Kurt Gödel.In 1931, he proved that every effectively generated theory capable of proving basic arithmetic either fails to be consistent or fails to be complete.
An incomplete sentence, or sentence fragment, is a set of words that does not form a complete sentence, either because it does not express a complete thought or because it lacks some grammatical element, such as a subject or a verb. [6] [7] A dependent clause without an independent clause is an example of an incomplete sentence.
The order with the comment sentence-initial is referred to as subjective (Vilém Mathesius invented the term and opposed it to objective) and expresses certain emotional involvement. The two orders are distinguished by intonation. In Modern Hebrew, a topic may follow its comment. For example, the syntactic subject of this sentence is an ...