To express the relation between one action and another, there exist some international icons. The basic operators you must know are , , , . The others are more complex, but here I put all of them as a reference, to be able to find them if you were searching any of them.

Symbol | It's read... | Description |
---|---|---|

or | is true whenever one of the two, or both, are true. | |

and | To make true, both and have to be true. | |

not | only is true when is false. | |

implies | Shows consequence. The expression says that when holds, so does . In addition, is considered true except for the case true and false. To understand that, think of an which implies and ask yourself: is it possible that is true but not ? Anyway, don't worry about that, it's not important right now. | |

if and only if | is the same as . It means that from we can deduce and viceversa, so they are equivalent. | |

false | The empty square represents false (the binary 0). Technically, it represents . | |

true | The filled square represents true (the binary 1). Technically, it represents . | |

exists... | can be read there exists an such that of . If in our domain, we can find an element (or more) which makes true the property applied to that element, then the formula is true. | |

for all... | can be read for all , of . If all elements we are working with make the property become true, then the formula is true. | |

then | is the symbol of the sequent, which is the way of saying ``when all this from the left happens, then it also happens all this from the right''. There exist valid sequents, like or like . But there are also invalid ones, like . The objective of natural deduction is to prove that a sequent is valid. | |

valid | means that is logical consequence of , but when one writes , what we mean is that the sequent is valid, that is, we could somehow prove it, and now is considered true for any interpretation of the predicate symbols. | |

invalid | means that is not logical consequence of . If you can find a series of values (model) which make true but false, then invalidity is proven. | |

satisfiable | A set of formulas is satisfiable if there exists a series of values (model) which can make all of them true at the same time. | |

unsatisfiable | A set of formulas is unsatisfiable if there isn't any combination of variables (model) which can make all of them become true at the same time. |

Daniel Clemente Laboreo 2005-05-17