We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences (...) of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect. (shrink)

In this paper we design a new logical system to explicitly model the different deductive reasoning steps of a boundedly rational agent. We present an adequate system in line with experimental findings about an agent’s reasoning limitations and the cognitive effort that is involved. Inspired by Dynamic Epistemic Logic, we work with dynamic operators denoting explicit applications of inference rules in our logical language. Our models are supplemented by (a) impossible worlds (not closed under logical consequence), suitably structured according to (...) the effect of inference rules, and (b) quantitative components capturing the agent’s cognitive capacity and the cognitive costs of rules with respect to certain resources (e.g. memory, time). These ingredients allow us to avoid problematic logical closure principles, while at the same time deductive reasoning is reflected in our dynamic truth clauses. We further show that our models can be reduced to awareness-like plausibility structures that validate the same formulas and we give a sound and complete axiomatization with respect to them. This approach to the agent’s internal deductive reasoning is finally combined with actions of external information. (shrink)

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...) between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

Orthodox Bayesianism is a highly idealized theory of how we ought to live our epistemic lives. One of the most widely discussed idealizations is that of logical omniscience: the assumption that an agent’s degrees of belief must be probabilistically coherent to be rational. It is widely agreed that this assumption is problematic if we want to reason about bounded rationality, logical learning, or other aspects of non-ideal epistemic agency. Yet, we still lack a satisfying way to avoid logical omniscience within (...) a Bayesian framework. Some proposals merely replace logical omniscience with a different logical idealization; others sacrifice all traits of logical competence on the altar of logical non-omniscience. We think a better strategy is available: by enriching the Bayesian framework with tools that allow us to capture what agents can and cannot infer given their limited cognitive resources, we can avoid logical omniscience while retaining the idea that rational degrees of belief are in an important way constrained by the laws of probability. In this paper, we offer a formal implementation of this strategy, show how the resulting framework solves the problem of logical omniscience, and compare it to orthodox Bayesianism as we know it. (shrink)

It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)