Intermediate Logic - Relation To Modal Logics

Relation To Modal Logics

Let A be a propositional formula. The Gödel–Tarski translation of A is defined recursively as follows:

If M is a modal logic extending S4 then ρM = {A | T(A) ∈ M} is a superintuitionistic logic, and M is called a modal companion of ρM. In particular:

  • IPC = ρS4
  • KC = ρS4.2
  • LC = ρS4.3
  • CPC = ρS5

For every intermediate logic L there are many modal logics M such that L = ρM.

Read more about this topic:  Intermediate Logic

Famous quotes containing the words relation to, relation and/or logics:

    “Only in a house where one has learnt to be lonely does one have this solicitude for things. One’s relation to them, the daily seeing or touching, begins to become love, and to lay one open to pain.”
    —Elizabeth Bowen (1899–1973)

    “Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
    —Ralph Waldo Emerson (1803–1882)

    “When logics die,
    The secret of the soil grows through the eye,
    And blood jumps in the sun;
    Above the waste allotments the dawn halts.”
    —Dylan Thomas (1914–1953)