Game Semantics, Quantifiers and Logical Omniscience

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there no consensus on how it should be restrained. The challenge conceptual: we must find adequate criteria separating obvious consequences (consequences which closure certainly holds) from non-obvious ones. Non-classical game-theoretic semantics has been employed discussion with relative success. On one hand, urn [15], an expressive fragment classical game weakens dependence relations between quantifiers occurring a formula, can formalize, broad array examples, scenarios individual ignores validity some first-order sentence. other offers disproportionate restriction omniscience. Therefore, improvement system needed to obtain better solution problem. In paper, I argue our linguistic competence using requires sort basic hypothetical formulated as follows: when inquiring after truth-value ∀xφ, might unaware all substitutional instances sentence accepts, but at least she know that, if element given, then ∀xφ holds only φ(x/a) true. This thesis accepts formalization terms refinement semantics. maintain so obtained (US+) affords improved To do this, characterize theoremhood US+. As consequence result, will see ideal reasoner depicted by US+ knows formulas whose Herbrand witnesses trivially found, fact provides strong evidence captures relevant sense obviousness.