Learn More
A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the "(More)
In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems based on finitely additive measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of(More)
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. The classic example is Public Announcement Logic (PAL), an extension of epistemic logic based on the idea of information acquisition as elimination of possibilities. In this paper, we address the open question of whether the set of schematic validities of(More)
We study possible algorithmic models for the picture verification task with double-quantified sentences of the form 'Some X are connected with every Y'. We show that the ordering of quantifiers, either Some • Every or Every • Some, influences the cognitive difficulty of the task. We discuss how computational modeling can account for the varying cognitive(More)
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known(More)
If knowledge required the elimination of all logically possible alternatives, there would be no knowledge (at least of contingent truths). There are always, it seems, possibilities that our evidence is powerless to eliminate. .. . If knowledge. .. requires the elimination of all competing possibilities. .. then, clearly we seldom, if ever, satisfy the(More)