Chapter 7: Formalisation of Predicate Logic
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7 Terms
A set Γ of 𝐿₂-sentences is syntactically consistent iff…
there is a sentence φ such that Γ ⊬ φ.
A set Γ of 𝐿₂-sentences is semantically consistent iff…
Γ is syntactically consistent.
The scope of an occurrence of a quantifier or a connective in a sentence φ of 𝐿₂ is…
the occurrence of the smallest 𝐿₂-formula that contains that occurrence of the quantifier or connective and is part of φ.
An English sentence is logically true in predicate logic iff…
its formalization in predicate logic is logically true.
An English sentence is a contradiction in predicate logic iff…
its formalisation in predicate logic is a contradiction.
A set of English sentences is consistent in predicate logic iff…
the set of their formalisations in predicate logic is semantically consistent.
An argument in English is valid in predicate logic iff…
its formalisation in the language 𝐿₂ of predicate logic is valid.