Modal definability in topology Master's thesis Acknowledgments During the year spent in Amsterdam at ILLC I have been lucky to be supported by many. The proper acknowledgment of everyone would have resulted in a separate book. I will only name a few, with the hope that the others will find my gratitude in between the lines. I am greatly indebted to Dr. Yde… (More)
The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of strong equivalence between logical programs that can be veriied in 3-valued GG odel logic, G3, the strongest non-classical intermediate propositional logic (Lifschitz, Pearce and Valverde, 2001). In this paper we… (More)
We extend Angluin's (1980) theorem to characterize identiiability of indexed families of r.e. languages, as opposed to indexed families of recursive languages. We also prove some variants characterizing conservativity a n d t wo other similar restrictions, paralleling Zeug-mann, Lange, and Kapur's (1992, 1995) results for indexed families of recursive… (More)
In this paper we consider preference over objects. We show how this preference can be derived from priorities, properties of these objects, a concept which is initially from optimality theory. We do this both in the case when an agent has complete information and in the case when an agent only has beliefs about the properties. After the single agent case we… (More)
This article ~s a report on research m progress into the structure of fimte diagrams of mtuinomst~c proposmonal logic with the aid of automated reasoning systems for larger calculanons. A/ragment of a proposmonal logic is the set of formulae built up from a fimte number of proposinonal variables by means of a number of connectives of the logic, among which… (More)
We investigate fragments of intuitionistic propositional logic containing implication but not disjunction. These fragments are finite, but their size grows superexponentially with the number of generators. Exact models are used to characterize the fragments.
We define preference in terms of a constraint sequence, a concept from optimality theory. In case agents only have incomplete information, beliefs are introduced. We propose three definitions to describe different procedures agents may follow to get a preference relation using the incomplete information. Changes of preference are explored w.r.t their… (More)
In this article we prove the Jankov Theorem for extensions of IPC () and the Jankov Theorem for KC () in a uniform frame-theoretic way in the setting of n-universal models for IPC. In frame-theoretic terms, the first Jankov Theorem states that for each finite rooted frame there is a formula ψ with the property that any counter-model for ψ needs this… (More)
abstract. In this article we study interpolation properties for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the £-modality easily follow from this result. Furthermore , these properties are extended to the system ILP. Failure of arrow interpolation for… (More)
This paper contains a completeness proof for the system ILW, a rather bewildering axiom system belonging to the family of interpretability logics. We have treasured this little proof for a considerable time, keeping it just for ourselves. Johan's fiftieth birthday appears to be the right occasion to get it out of our wine cellar.