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J. Alama:
"Without E";
accepted as talk for: Logica 2014, Hejnice, Tschechien; 2014-06-17 - 2014-06-20.

Dialogue games are a two-player game-based semantics for a variety of logics. The Proponent (P) asserts an initial formula F; the Opponent (O) disputes that F is valid. The players take turns, attacking or defending logical formulas. There are a few ways in which dialogues can be defined. There seems to be no unique formalization, though one can clearly see family resemblances among them. One rule that comes up often is the so-called E rule, which says that O must respond to P's immediately preceding move. The E rule is regarded as awkward and lacking a clear significance in any ordinary sense of "dialogue". Its sole value appears to be that it facilitates proofs of adequacy (soundness and completeness). While acknowledging its utility, one might naturally wish to eliminate the E rule, or at least replace it by a rule that has intuitively greater plausibility. In some contexts, it is known that E is in fact redundant (a set of rules with E has the same logical force as the ruleset without E), while in other contexts, E seems to be essential. Toward that end, this note investigates a dialogical characterization of classical logic in which the E rule is relaxed.