Validity in a presheaf ‘F’ over a topological space can be defined via a forcing relation between points and formulas, similarly to Kripke semantics. An isomorphism is an invertible morphism. A presheaf over a locale Ω is defined as a functor. The connection between presheaves and Ω-sets is well known in topos theory. An equivalent representation of algebraic semantics using presheaves is considered. Maps between algebraic structures preserving validity are analogues of p-morphisms used in propositional logic. A formula ‘A’ is valid in a structure ‘F’ if ‘A’ is true in every model over ‘F’. For a structure F, an n-ary F-predicate is a map. Every propositional Kripke frame ‘F’ corresponds to a modal algebra MA (F), so Kripke semantics is treated as a particular case of algebraic semantics.
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