Forces (⊩) Relation in Modal Logic { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies, and introductions to philosophers, and explanations on a number of topics. Accredited homeschooling online at Northgate Academy and Philosophy online tutoring.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WTI offers immigration law course online - fully accredited. ACE credits online at EES.

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Forces (⊩)

The logical relation (⊩), normally read as “forces” is a relationship between a possible world of modal logic, and some proposition or predicate sentence in that world.

The relation ⊩ is the third member of a modal model — a logical object that consists of some set of possible worlds, some accessibility relationship between those worlds, and the relation ⊩ which describes which propositions or predicate terms are true in which worlds.

Ultimately, if we have some possible world, Δ, then we may express that some proposition, P, is true in that world by Δ ⊩ P. This may be read as “Δ forces P”, which is to say that P, which would generally be either possible or neccessary with respect to all possible worlds, becomes actually true in the possible world Δ

To indicate that a possible world does not force a proposition or formula, we use the symbol ⊮. So if Γ ⊩ ¬P, then Γ ⊮ P.