Karl Schlechta

FLAP Journal 2023 Journal Article

On Yablo's Construction.

• Karl Schlechta

We analyse Yablo’s coding of the liar paradox by infinite acyclic graphs, [6], and show that his construction is in a certain way minimal. This leads to a very limited representation result. We then argue that the “right” level of description of more complicated constructions is probably the level of paths, and not of single arrows. We also look at more complicated cells of basic contradiction ("diamonds"), and show that, at least under certain conditions, they fail to achieve Yablo’s result.

TCS Journal 2001 Journal Article

Explaining updates by minimal sums

• Karl Schlechta
• Jürgen Dix

Human reasoning about developments of the world involves always an assumption of inertia. We discuss two approaches for formalizing such an assumption, based on the concept of an explanation: (1) there is a general preference relation ≺ given on the set of all explanations and (2) there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal. Each distance dist naturally induces a preference relation ≺ dist. We show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions. Our main result is a general representation theorem in the spirit of Kraus, Lehmann and Magidor.

TARK Conference 1996 Conference Paper

Distance Semantics for Belief Revision

• Karl Schlechta
• Daniel Lehmann 0001
• Menachem Magidor

A vast and interesting family of natural semantics for Belief Revision is defined. Suppose one is given a distance d between any two models. One may define the revision of a theory K by a formula a as the theory defined by the set of all those models of a that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.

AIJ Journal 1991 Journal Article

Floating conclusions and zombie paths: Two deep difficulties in the “directly skeptical” approach to defeasible inheritance nets

• David Makinson
• Karl Schlechta

We discuss two difficulties in the “directly skeptical” approach to inference in defeasible inheritance nets, as developed by Horty, Thomason and Touretzky. We suggest that as a result of the general architecture of the approach, it is intrinsically unable to deal with a phenomenon of “floating conclusions”, and has great difficulty in accommodating a phenomenon of “zombi paths”. The conclusion drawn is that the directly skeptical approach cannot hope to do the work of an approach via the family of all extensions.

ECAI Conference 1990 Conference Paper

Semantics for Defeasible Inheritance

• Karl Schlechta