Knowledge and Belief in Distributed Systems
Ante Debeljuh
"Epistemic and doxastic logics were developed as a way of talking about knowledge and belief attribution in the most abstract of settings. Hintikka’s endeavour (1963) resulted in this domain-specific formalism reflecting the behaviour of epistemic and doxastic notions within its theoretical framework. The basis for this development was modal logic with intensional semantics, which allowed the theorists to construct the notions of knowledge and belief through relational structures. The theorists’ attempts of calibrating the formalism to fit the epistemic theory and vice versa resulted in what we now know as epistemic modelling. Keeping this in mind, there appeared quite a few of theoretical frameworks that diverged in the way that the basic constituents of epistemic models were defined. The earlier attempts were predominantly language-based, which used structures such as sentences to play the part of the basic units of the model. I will use Stalnaker’s paper The Problem of Logical Omniscience I to elaborate a bit on the model he dubbed The Sentence Storage Model in order to examine some prominent issues the theorists encounter when constructing a language-based model. Some later attempts of constructing a non-linguistic model were inspired by computer sciences and developed into proper epistemic models that avoided many of the problems that the language-based models encountered. Stalnaker wrote another paper named On the Logics of Knowledge and Belief, in which he discusses such attempts of model building. The specific framework for modelling that I intend to discuss in my talk is called Distributed Systems Modelling (DSM), that adapts the way of talking about interconnected processors within a computer network into an externalist epistemic model. I intend to show how we can adapt the language that epistemic logics use to talk about knowledge and belief to the DSM jargon in order to show how this way of conceptualizing epistemic situations can be a useful theoretical instrument. Furthermore, I intend to talk about the interrelationship between knowledge and belief within such structures as DSMs, as not all logics used in epistemic modelling are capable of defining them discretely. I intend to skim through some formalisms such as S4, S4.2, and S5 in order to show how this interrelationship can be defined."
