Logic and Games
Updated 2026-09-10
INTRODUCTION
English translation pending.
CORE DEFINITION
In the second half of the twentieth century, two-player games in which one side wins and the other loses became a common tool in many branches of logic. Important examples include semantic games used to define truth, back-and-forth games used to compare structures, and dialogue games used to express and explain formal proofs. In each case a logical notion is analyzed through winning strategies.
SCAFFOLDING EFFECT
Reduce cognitive load
- Argue by play: break an argument into an attack-and-defense match between two sides and see who holds a winning strategy. - Compare structures: use a game in which players pick elements in turn to test whether two structures can be told apart. - Clarify semantics: redefine truth as winnability in a game and thereby avoid a circular definition.
Anchor fast decisions
Game semantics defines truth as an existential fact about a game: the verifier tries to confirm the formula and the falsifier tries to refute it, and the formula is true just in case the verifier has a winning strategy. Back-and-forth games compare two structures by having players pick elements in turn, and if the duplicator can always match the opponent's choices the structures are indistinguishable in the corresponding language.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- plato.stanford.eduhttps://plato.stanford.edu/entries/logic-games/verified
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