arXiv subjects
Publications and source records attributed to Karl Schlechta.
We continue our analysis of Yablo's coding of the liar paradox by infinite acyclic graphs. The present notes are based on and continue the author's previous results on the problem. In particular, our approach is often more systematic than before.
This is a sequel to the author's "Truth and Knowledge", College Publications, 2022, and contains some problems and results in connection with a possible representation for Yablo like structures.
The main subjects of this text are: (1) Generalization of concepts and operations, like distance and size, to situations where they are not definable in the usual way. (2) A pragmatic theory of handling contradictions using reliability of the information sources. (3) Relation of formal semantics to brain processes. (4) Remarks on Yablo's coding of the liar paradox in infinite acyclic graphs.
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
We interpret homogenousness as a second order property and base it on the same principle as nonmonotonic logic: there might be a small set of exceptions. We use this idea to analyse fundamental questions about defeasible inheritance systems. In an appendix, we discuss the concept of the core of a (model) set.
This is a short (and personal) introduction in German to the connections between artificial intelligence, philosophy, and logic, and to the author's work. Dies ist eine kurze (und persoenliche) Einfuehrung in die Zusammenhaenge zwischen Kuenstlicher Intelligenz, Philosophie, und Logik, und in die Arbeiten des Autors.
We define analogues of Boolean operations on not necessarily complete partial orders, they often have as results sets of elements rather than single elements. It proves useful to add to such sets X if they are intended to be sup(X) or inf(X), even if sup and inf do not always exist. We then define the height of an element as the maximal length of chains going from BOTTOM to that element, and use height to define probability measures.
We show that conjecture 15 in the article by Rabern et al. is wrong, comment on theorem 24 there, and conclude with some remarks on structures similar to the Yablo construction.
Our approach is basically a coherence approach, but we avoid the well-known pitfalls of coherence theories of truth. Consistency is replaced by reliability, which expresses support and attack, and, in principle, every theory (or agent, message) counts. At the same time, we do not require a priviledged access to "reality". A centerpiece of our approach is that we attribute reliability also to agents, messages, etc., so an unreliable source of information will be less important in future. Our ideas can also be extended to value systems, and even actions, e.g., of animals.
The elegant Stalnaker/Lewis semantics for counterfactual conditonals works with distances between models. But human beings certainly have no tables of models and distances in their head. We begin here an investigation using a more realistic picture, based on findings in neuroscience. We call it a pre-semantics, as its meaning is not a description of the world, but of the brain, whose structure is (partly) determined by the world it reasons about. In the final section, we reconsider the components, and postulate that there are no atomic pictures, we can always look inside.
We use the theory of defaults and their meaning of [GS16] to develop (the outline of a) new theory of argumentation.
We investigate several technical and conceptual questions. Our main subject is the investigation of independence as a ternary relation in the context of non-monotonic logic. In the context of probability, this investigation was started by W.Spohn et al., and then followed by J.Pearl. We look at products of function sets, and thus continue our own investigation of independence in non-monotonic logic. We show that a finite characterization of this relation in our context is impossible, and indicate how to construct all valid rules.
In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.
We offer a technical analysis of the contrary to duty system proposed in Carmo-Jones. We offer analysis/simplification/repair of their system and compare it with our own related system.
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.