Language is essentially a translation between a thought and a physical correlate such as speech, signing, or writing. This translation is mediated in both directions by the computational system known as syntax or grammar. The Logical Form (LF) is the syntactic representation that interfaces with the conceptual and intentional apparatus (C-I), while the Phonetic Form (PF) is the representation that interfaces with articulatory and perceptual systems (A-P). Minimally, a language must have LF, PF, and a language-specific system of rules for relating them.

The term 'logical form' is also used in logic and in semantics, without the implication of its being a precise syntactic level. Here I am concentrating on Chomsky's syntactic notion of LF. The two should, of course, at least roughly coincide.

Different languages have extremely different methods of marking their grammar: word order, case and agreement, possibilities for reference binding and quantification, and so on. Yet as far as we know all human beings have essentially the same mental endowment. Moreover, any baby born anywhere automatically learns its native language perfectly within a few years, long before it can master most intellectual tasks. Therefore it is widely believed that there is a genetically determined language faculty, and a Universal Grammar that is its default setting. Principles and Parameters theory holds that there are fundamentally similar principles underlying all languages, and exposure to a particular language sets the parameters that distinguish that from other grammars, producing different representations at PF.

However, since LF interfaces with C-I, and C-I is the same for all people, LF is much more constrained in how it can be. At some level, all languages must have the same grammar. This grammar can be translated into the Language of Thought, the non-linguistic means (whatever it may be) by which we manipulate concepts and understand connexions. So where languages differ in their parameters, at some point those differences must be overcome.

A sentence is built up as a syntactic structure by general rules, the scope of whose application in a particular language is determined by its parameters. The contents have phonetic form which is arbitrary, and specific to the language. At some point the surface form of the sentence is completely built, and it can be spelt out as its pronunciation. This stage is called Spell-Out. Rules of the language's phonology apply to it at the PF stage for it to be pronounced.

The grammar has at this stage generated a complex, idiosyncratic structure with the word order and marking specific to that language. To be comprehensible it has to continue on to Logical Form. Grammars differ in how parameters are set for common principles. They also differ in the words in their lexicon, but once Spell-Out has happened the phonetic part of the words has gone off in a separate direction, and what remains to be interpreted is the syntactic structure and its semantic content. So we have a semantic or logical structure jumbled by a particular choice of syntactic parameters.

Therefore to proceed to Logical Form it is necessary to operate on all the parameters so as to bring them into a universal format. Syntactic operations such as movement and checking keep happening in the passage from Spell-Out to LF, but now they do it covertly, purely to satisfy the logic of it, and can no longer affect how the sentence appears phonetically.

One example is quantification. The sentences Someone speaks every language in the world and None of the children brought some of the books are ambiguous in the scope of the quantifiers. It is believed that at LF the quantifiers are brought up to the front in the required order, and this determines the interpretation.

Another example is WH-fronting. In English and many languages questions are asked by bringing an element to the front: Mary talked to someone. ~ Who did Mary talk to? The WH-word is logically similar to a quantifier. However, Chinese and Japanese do not move their WH-words: they are known as WH-in-situ languages. In English we can preserve this order in echo questions and quiz questions: Mary talked to who? But it is believed that even when the WH-word is kept in situ in the phonetic representation, covert movement of it to the front takes place in order for it to be understood.

Many other movements are regarded as necessary, even if they don't appear important to a language. Verbs need to check off agreement with their subject and object, though many languages don't mark this overtly on their verbs. Still, in order to reduce grammar to relatively few logical principles that a young child can pick up, the underlying grammar should be as simple as possible, so a rule that says to always move verbs for agreement checking exists in all languages. They differ in the strength of the parameter: a strong feature is one that moves overtly for checking, producing a difference in PF, while a weak feature is checked by covert movement from Spell-Out to LF.