Jürgen Landes

Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic

We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum exchangeability in polyadic inductive logic and give an application by characterizing those probability functions satisfying spectrum exchangeability which can be extended to a language with equality whilst still satisfying that property.

Objective Bayesianism and the Maximum Entropy Principle

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.

Some Aspects of Polyadic Inductive Logic

We give a brief account of some de Finetti style representation theorems for probability functions satisfying Spectrum Exchangeability in Polyadic Inductive Logic, together with applications to Non-splitting, Language Invariance, extensions with Equality and Instantial Relevance.

A characterization of the language invariant families satisfying spectrum exchangeability in polyadic inductive logic

A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.

Min–max decision rules for choice under complete uncertainty: Axiomatic characterizations for preferences over utility intervals

Abstract We introduce two novel frameworks for choice under complete uncertainty. These frameworks employ intervals to represent uncertain utility attaching to outcomes. In the first framework, utility intervals arising from one act with multiple possible outcomes are aggregated via a set-based approach. In the second framework the aggregation of utility intervals employs multi-sets. On the aggregated utility intervals, we then introduce min–max decision rules and lexicographic refinements thereof. The main technical results are axiomatic characterizations of these min–max decision rules and these refinements. We also briefly touch on the independence of introduced axioms. Furthermore, we show that such characterizations give rise to novel axiomatic characterizations of the well-known min–max decision rule ≽ mnx in the classical framework of choice under complete uncertainty.

A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic

We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.

Instantial Relevance in Polyadic Inductive Logic

We show that under the assumptions of Spectrum Exchangeability and Language Invariance the so called Only Rule , a principle of instantial relevance previously know for unary (i.e. classical) Carnapian Inductive Logic, also holds in Polyadic Inductive Logic.

Special issue: Combining probability and logic

The papers appearing in this special issue arose out of the seventh workshop on Combining Probability and Logic, Progic 2015. This workshop, which took place in April 2015 at the University of Kent, had a special focus on formal epistemology and inductive logic. The accepted papers fall into three main categories: inductive logic in the spirit of Rudolf Carnap; probability logics; and many-valued logics.

Argumentation–Based Negotiation? Negotiation–Based Argumentation!

We design a protocol for two autonomous negotiating agents to incorporate Dung-style argumentation into an ongoing bargaining dialogue. Previous approaches considered bargaining and Dung-Style Argumentation as separated components, we show that intertwining these approaches increases the agents scope of action. In our framework the acceptance of an argument or attack uttered by self-interested agents is conditional on the acceptance by the negotiating partner. Our protocol thus enables autonomous agents to engage in a variety of human negotiation behaviours and thereby increase the agents capabilities to come to mutually satisfactory agreements.

Language Invariance and Spectrum Exchangeability in Inductive Logic

A sufficient condition, in terms of a de Finetti style representation, is given for a probability function in Inductive Logic (with relations of all arities) satisfying Spectrum Exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions. In contrast it is proved that (purely) t-heterogeneous probability functions can never be members of a language invariant family satisfying Spectrum Exchangeability.