MCMP Curated Collections

Nonmonotonic and Epistemic Logics
Hand-Picked by Holger Andreas

Classical logic is monotonic in the following sense. Suppose we have a logically valid argument from a set P of premises to a conclusion C. Then, any additional premise does not invalidate this argument. We can add as many premises as we want, without altering the validity of the argument. This condition, however, proved too restrictive for a logical analysis of everyday reasoning. In such non-mathematical contexts, we make use of nonmonotonic arguments quite frequently. That is, we use arguments that are invalidated by additional premises. In yet other words, we use defeasible arguments. These arguments are based on default axioms or default rules, which work in a fairly reliable way, but do a have a few exceptions. Nonmonotonic logics have thus been devised to study nonmonotonic arguments. These logics originated from computer science, but their relevance to philosophical questions was recognized soon by logicians working in philosophy.Dynamic epistemic logics, on the other hand, aim at a modal logic analysis of belief changes. As in nonmonotonic reasoning some conclusion may be defeated by an additional premise, so may some of our beliefs become retracted by further information. Belief revision and nonmonotonic reasoning thus turned out to be highly interrelated.
Reasoning Biases

Catarina Dutilh Novaes shows how nonmonotonic logics can be used to analyse reasoning biases.

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Truth-Conduciveness

There is a surprisingly large number of methods of how we can change our beliefs. Logicians distinguish more than 20 different methods. Sonja Smets investigates–for a selection of putatively canonical methods–which of these methods are truth-conducive.

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Ordering Beliefs and Bayesian Updating

Alexandru Baltag addresses the same question as Sonja Smets, while paying particular attention to the epistemic ordering of beliefs. Moreover, he compares belief updating with Bayesian updating, the latter being a probabilistic approach to the dynamics of our epistemic states.

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Adaptive Logics

Peter Verdée presents the stunning system of adaptive logics, the first adaptive logic that comes with a fully fledged proof-theory. Besides the primary target of everyday defeasible reasoning, adaptive logics proved useful to model also abductive, inductive and paraconsistent reasoning.

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Qualitative vs Quantitative Approaches

Michiel van Lambalgen invites us to ask the question of whether quantitative or qualitative approaches to the dynamics of our epistemic states are cognitively more appropriate. He presents empirical evidence in favour of the former.

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Possible Worlds Models

Hans Rott gives a very intricate talk about possible worlds models of epistemic state, as a result of which he suggests a modification in a belief change model favoured by J. Halpern.

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The Dynamic Epistemic Framework I

Hans van Ditmarsch exploits the dynamic epistemic framework to deal with the Moore-sentence, 'p is true but you don't know that p is true', and also the Fitch-paradox, 'everything is knowable', is inconsistent. He unfolds a reading on which these sentences cease to be paradoxical.

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The Dynamic Epistemic Framework II

Barteld Kooi addresses the problem of logical omniscience in terms of a neighbourhood semantics, which of course is also the dynamic epistemic framework.

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Conditionals and Social Choice Theory

At the outset, Peter Gärdenfors' work on belief changes was motivated by an epistemic semantics of conditionals which promised to be cognitively more plausible than the standard semantics of conditionals by David Lewis. However, at a later stage he discovered an impossibility theorem concerning the particular semantics he happened to have developed. Hannes Leitgeb shows how this theorem is related to an impossibility theorem in social choice theory.

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I hope you enjoyed this collection–thanks for watching! Holger