Logical form

Logical form is a representation of all and only the logical properties of an expression, usually in a non-ambiguous, precise logical language. The term was originally used in opposition with grammatical form, the idea being that the grammatical form of a sentence is often misleading with respect to its logical properties, for example in the case of definite descriptions.

Link

Utrecht Lexicon of Linguistics

Syntax

a distinct, structural level of representation, usually abbreviated as LF (see T-model), which contains all (and only) the syntactic information that is relevant for semantic interpretation. LF is thus taken to be the interface between an expression (language) and its logical form (in the semantic sense). LF is derived from S-structure through instances of affect alpha, e.g. Quantifier Raising and Wh-raising (see Wh-in-situ).

Example

sentence (i) can either mean that there is a particular girl that I want to kiss or that I want to kiss any girl. In semantics, this ambiguity can be captured by associating the sentence with the two logical forms (ii)a and b. In syntax, the sentence is represented at the level of LF as in (iii)a and b. In both analyses the ambiguity is taken to be one of scope of the Quantifier relative to the modal verb: either a girl has scope over want, or want has scope over a girl.

(i)	 I want to kiss a girl
(ii)  a	 there is an x, x=a girl, such that I want to kiss x
      b	 I want there to be an x, x=a girl, such that I kiss  x
(iii) a	 [ a girli [I want [ PRO to kiss ti ]]]
      b	 [ I want [ a girli [ PRO to kiss ti ]]]