Re: Can propositions be classified into type-n?

On Apr 7, 2:35 pm, sip...@xxxxxxxxx wrote:
Given that propositional calculus deals with propositions, can the
propositions be classified into any in Chomsky hierarchy? Aren't
propositions generative grammars?

Items that can be placed in the Chomsky hierarchy are languages (which
are sets of strings, usually defined using a grammar or machine).

Propositional calculus is a computational mechanism for determining
truth. It is usually presented with a syntax (a grammar) that is
fairly simple (variables, and, or not, true false, and parens), where
the parens or implicit precedence of operators require a context-free
grammar.

The language (syntax rules) of PC is context free.

So particular propositions cannot really be placed in the Chomsky
hierarchy, but a given logic (like propositional calculus) has a
syntax that can be placed there.

The importance of PC is not in its language but in the truth functions
it can describe.

Mitch
.

Relevant Pages

  • Re: Can propositions be classified into type-n?
    ... propositions be classified into any in Chomsky hierarchy? ... Items that can be placed in the Chomsky hierarchy are languages (which ... usually defined using a grammar or machine). ... The language of PC is context free. ...
    (comp.theory)
  • Can propositions be classified into type-n?
    ... Given that propositional calculus deals with propositions, ... propositions be classified into any in Chomsky hierarchy? ...
    (comp.theory)