Search results
Results From The WOW.Com Content Network
Modal logic is a kind of logic used to represent statements about necessity and possibility.It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation.
Modal logic concerns the manner, or mode, in which statements are true. Contingency is one of three basic modes alongside necessity and possibility. In modal logic, a contingent statement stands in the modal realm between what is necessary and what is impossible, never crossing into the territory of either status.
Modal logics include additional modal operators, such as an operator which states that a particular formula is not only true, but necessarily true. Although modal logic is not often used to axiomatize mathematics, it has been used to study the properties of first-order provability [39] and set-theoretic forcing. [40]
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
[1] [8] One problem for this type of characterization is that they seem to be circular since possible worlds are themselves defined in modal terms, i.e. as ways how things could have been. [8] Even when restricted to alethic modal logic, there are again different types of possibility and necessity that can be meant by these terms.
The basic question about admissible rules of a given logic is whether the set of all admissible rules is decidable. Note that the problem is nontrivial even if the logic itself (i.e., its set of theorems) is decidable : the definition of admissibility of a rule A / B involves an unbounded universal quantifier over all propositional substitutions.
The modal base here is the knowledge of the speaker, the modal force is necessity. By contrast, (5) could be paraphrased as 'Given his abilities, the strength of his teeth, etc., it is possible for John to open a beer bottle with his teeth'. Here, the modal base is defined by a subset of John's abilities, the modal force is possibility.