Norbert Preining

Continuous Fraïssé Conjecture

We will investigate the relation of countable closed linear orderings with respect to continuous monotone embeddability and will show that there are exactly

Gödel Logics and Cantor-Bendixon Analysis

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Hyper Natural Deduction

many equivalence classes with respect to this embeddability relation. This is an extension of Laver’s result (Laver, Ann. Math. 93(2):89–111, 1971), who considered (plain) embeddability, which yields coarser equivalence classes. Using this result we show that there are only

SAT in Monadic Gödel Logics: A Borderline between Decidability and Undecidability

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First-order satisfiability in Gödel logics: An NP-complete fragment

many different Gödel logics.

Gödel logics: a survey

This paper presents an analysis of Godel logics with countable truth value sets with respect to the topological and order theoretic structure of the underlying truth value set. Godel logics have taken an important role in various areas of computer science, e.g. logic programming and foundations of parallel computing. As shown in a forthcoming paper all these logics are not recursively axiomatizable. We show that certain topological properties of the truth value set can distinguish between various logics. Complete separation of a class of countable valued logics will be proven and direction for further separation results given.

Separating intermediate predicate logics of well-founded and dually well-founded structures by monadic sentences

We introduce a Hyper Natural Deduction system as an extension of Gentzens Natural Deduction system. A Hyper Natural Deduction consists of a finite set of derivations which may use, beside typical Natural Deduction rules, additional rules providing means for communication between derivations. We show that our Hyper Natural Deduction system is sound and complete for infinite-valued propositional Gödel Logic, by giving translations to and from Avrons Hyper sequent Calculus. We also provide conversions for normalisation and prove the existence of normal forms for our Hyper Natural Deduction system.

Deciding logics of linear Kripke frames with scattered end pieces

We investigate satisfiability in the monadic fragment of first-order Gadel logics. These are a family of finite- and infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing 0 and 1. We identify conditions on the topological type of V that determine the decidability or undecidability of their satisfiability problem.

An Empirical Illustration to Validate a FLOSS Development Model Using S-Shaped Curves

Defined over sets of truth values V which are closed subsets of [0,1] containing both 0 and 1, Godel logics GV are prominent examples of many-valued logics. We investigate a first-order fragment of GV extended with @D, that is powerful enough to formalize important properties of fuzzy rule-based systems. The satisfiability problem in this fragment is shown to be NP-complete for all GV, also in the presence of an additional, involutive negation. In contrast to the one-variable case, in the fragment considered, only two infinite-valued Godel logics extended with @D differ w.r.t. satisfiability. Only one of them enjoys the finite model property.

Linear Kripke frames and Gödel logics

The logics we present in this tutorial, Godel logics, can be characterized in a rough-and-ready way as follows: The language is standard, defined at different levels: propositional, quantified-propositional, first-order. The logics are many-valued, and the sets of truth values considered are (closed) subsets of [0, 1] which contain both 0 and 1. 1 is the ‘designated value,’ i.e., a formula is valid if it receives the value 1 in every interpretation. The truth functions of conjunction and disjunction are minimum and maximum, respectively, and in the first-order case quantifiers are defined by infimum and supremum over subsets of the set of truth values.