Formalization of Arguments

Circular Arguments, Begging the Question and the Formalization of Argument Strength

Recently Oaksford and Hahn (2004) proposed a Bayesian reconstruction of a classic argumentation fallacy Locke’s ‘argument from ignorance.’ Here this account is extended to what is probably the most well-known of all argumentation fallacies: circular reasoning or ‘begging the question’. A Bayesian analysis is shown to clarify when and where circular reasoning is good or bad, and how seeming para...

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Real Arguments Are Approximate Arguments

There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logic-based argumentation is that an argument is a pair 〈Φ, α〉 where Φ is minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claim α. However, real argument...

The formalization of Interpretability

Formalization of Generative Unbinding

Pitts and Shinwell introduced an idealized programming language containing constructs for binding and also for pattern matching against this binding construct. They prove a result about which operations on names can co-exist with the binding construct in this language. What makes this construct interesting is that it generates a new name at the moment of “unbinding”. In this report we describe ...