Reasoning about Rational, but not Logically Omniscient Agents

We propose in the paper a new solution to the so-called Logical Omniscience Problem of epistemic logic. Almost all attempts in the literature to solve this problem consist in weakening the standard epistemic systems: weaker systems are considered where the agents do not possess the full reasoning capacities of ideal reasoners. We shall argue that this solution is not satisfactory: in this way omniscience can be avoided, but many intuitions about the concepts of knowledge and belief get lost. We shall show that axioms for epistemic logics must have the following form: if the agent knows all premises of a valid inference rule, and if she thinks hard enough, then she will know the conclusion. To formalize such an idea, we propose to \dynamize' epistemic logic, that is, to introduce a dynamic component into the language. We develop a logic based on this idea and show that it is suitable for formalizing the notion of actual, or explicit knowledge

Dynamic Epistemic Logic and Logical Omniscience

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience

Did the market-clearing postulate pre-exist new classical economics ? The case of Marshallian theory

Have new classicists invented market clearing or have they rehabilited it ? This is the question addressed in the present paper. It is generally agreed that market clearing underpins Walrasian theory, so my exploration is limited to the question of whether this is also true for Marshallian theory. I will claim that this is broadly the case : once Marshallian theory is properly reconstructed, it exhibits market clearing as a constantly present result. Still; an important difference between market à la Walras and market clearing à la Marshall exists : in the former market clearing is equilibrium, while in the latter market clearing can coexist with disequilibrium. Next, I investigate whether my conclusion extends to the labour market. Again the conclusion reached is affirmative both for Marshall’s theory and for present-day Marshallian models. As to the latter, I take Friedman’s Phillips Curve model as a case study. I show that this is a market clearing model in which, strictly speaking, there is no place for the concept of unemployment - quite an ironical result for the paper that introduced the notion of the natural rate of unemployment !market clearing; equilibrium; Lucas; Marshall; Friedman

Expressing Belief Flow in Assertion Networks

Abstract. In the line of some earlier work done on belief dynamics, we propose an abstract model of belief propagation on a graph based on the methodology of the revision theory of truth. A modal language is developed for portraying the behavior of this model, and its expressiveness is discussed. We compare the proposal of this model as well as the language developed with some of the existing frameworks for modelling communication situations.

Animals and the Problem of Evil in Recent Theodicies

This paper critically evaluates the theodicies of John Hick, Richard Swinburne and process theism regarding animal suffering and evils. The positions of Hick and Swinburne are based on false empirical assumptions, e.g., animals do not suffer. Process theism’s claim that God is not omnipotent is an unsatisfactory answer inconsistent with the traditional concept of God. These positions cannot fully explain the mass suffering and unnecessary deaths of animals throughout time. My positive position is that God’s putative love for all sentient beings does not necessarily entail that he loves every individual human and animal. Humans do not interfere with the suffering and deaths of animals in the wild, and God has no obligation to interfere with human evils. It is very possible that God acts similarly with humans and animals regarding evils. This theory partly explains human tragedies such as the Holocaust and much unnecessary animal and human suffering