The generic modal reasoner CoLoSS covers a wide variety of logics ranging from graded and probabilistic modal logic to coalition logic and conditional logics, being based on a broadly applicable coalgebraic semantics and an ensuing general treatment of modal sequent and tableau calculi. Here, we present research into optimisation of the reasoning strategies employed in CoLoSS. Specifically, we ...

We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability a...

We present a probabilistic extension of the description logic ALC for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical consequences of these proportions. After introducing some general reasoning problems and analyzing their properties, we present first algorithms and complexity results for re...

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general 'thinking skills'. Today, this argument, known as the 'Theory of Formal Discipline' is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by ...

We present a probabilistic extension of the description logic ALC for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical consequences of these proportions. After introducing some general reasoning problems and analyzing their properties, we present first algorithms and complexity results for re...

In this paper we analyze the conditional logic approach to default logic, the logic that formalizes reasoning about default assumptions.Conditional logic is a popular framework to formalize defeasible reasoning. The conditional sentence “if (the antecedent or condition) then by default (the consequent or conclusion)” is represented in this framework by the formula > , where ‘>’ is some kind of ...

In many domains it is desirable to assess the preferences of users in a qualitative rather than quantitative way. Such representations of qualitative preference orderings form an important component of automated decision tools. We propose a graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else bei...

An approach to nonmonotonic inference based on a closure operation on a conditional knowledge base is presented The central idea is that, given a theory of default conditionals, an extension to the theory le defined that satisfies certain intuitive restrictions Two notions for forming an extension are given, corresponding to the incorporation of irrelevant properties in conditionals and of tran...

Ramsey’s test for conditionals seems to be in conflict with the so-called Thomason conditionals. A Thomason conditional is a conditional in which either the antecedent or the consequent is a statement about the reasoning agent’s own beliefs. Several authors have pointed out that resolving the apparent conflict is to be sought by abandoning the belief revision interpretation of the Ramsey test i...

There are two accounts explaining how background information can affect the conditional reasoning performance: the probabilistic account and the mental model account. According to the mental model theory reasoners retrieve and integrate counterexample information to attain a conclusion. According to the probabilistic account reasoners base their judgments on likelihood information. It is assume...