lobispan.blogg.se - Ways to use the modal logic playground

While it is logically possible to travel faster than the speed of light, it is not, according to modern science, physically possible. On the other hand, it is not possible, in this sense, for there to be an element whose nucleus contains cheese. For example, it is possible for there to be an atom with an atomic number of 150, though there may not in fact be one. Something is physically possible if it is permitted by the laws of nature. For example, it is necessary that if Elvis is alive, then he is alive. Something which is logically necessary is called a logical truth. Many logicians also hold that mathematical truths are logically necessary: it is impossible that 2+2 ≠ 4. It is possible that Elvis is alive but it is impossible that Elvis is alive and is not alive. Likewise, almost nothing is logically impossible: something logically impossible is called a contradiction or a logical falsehood.

There are a number of different alethic modalities: logical possibility is, perhaps, the weakest, since almost anything intelligible is logically possible: Possibly, pigs can fly, Elvis is still alive, and the atomic theory of matter is false. Thus if something is necessarily true, then it is true if it is true, then it is possible. It could have been otherwise, so it is possibly true, and possibly false.

contingent if it is actually true, but not necessarily true.

necessary if it could not possibly be false.

possible if it might be true (regardless of whether it is or is not actually true).

For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as the subject matter of modal logic. Modal logic was first developed to deal with these concepts, and only afterward was extended to others. Necessity and possibility are sometimes called alethic modalities, from the Greek aletheia, truth.

1.4 Confusion with epistemic modalities.

Thus it is possible that Jones was murdered if and only if it is not necessary that Jones was not murdered. Each can be defined from the other and negation. The basic modal operators are usually (or L) for Necessarily and (or M) for Possibly. For example, "Jones's murder was a possibility" "Jones was possibly murdered" and "It is possible that Jones was murdered," all contain the notion of possibility in a modal logic this is represented as an operator, Possibly, attaching to the sentence Jones was murdered. Logics for handling a number of other ideas, such as eventually, formerly, can, could, might, may, must are by extension also called modal logics, since it turns out that these can be treated in similar ways.Ī formal modal logic represents modalities using unary modal operators.

Finally, we consider some domain-specific control heuristics that are useful for doing deductions in this formalism, and we present several examples of deductions produced by applying these heuristics.In philosophical logic, a modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. We use these notions to express what knowledge a person must have in order to perform a given action and what knowledge a person acquires by carrying out a given action. We integrate this theory with a logic of actions by identifying possible worlds with the situations before and after an action is performed. This means that we reason not about what facts someone knows, but rather what possible worlds are compatible with what he knows. We solve this problem by taking the possible-world semantics for a modal logic of knowledge and axiomatizing it directly in first-order logic. There are, however, no known techniques for efficiently doing automatic deduction directly in modal logics. The first problem we face in achieving this goal is that the basic facts about knowledge we need to use are most naturally expressed as a modal logic. In particular, we want to be able to reason about what knowledge a person must have in order to perform an action, and what knowledge a person may gain by performing an action. This report deals with the problem of making a computer reason about the interactions between knowledge and action.