Related papers: Ordinal Notation
We survey some basic mathematical structures, which arguably are more primitive than the structures taught at school. These structures are orders, with or without composition, and (symmetric) monoidal categories. We list several `real life'…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.…
We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to M, and also an elementary submodel of M for infinitary…
We propose a coreference annotation scheme as a layer on top of the Universal Conceptual Cognitive Annotation foundational layer, treating units in predicate-argument structure as a basis for entity and event mentions. We argue that this…
Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear…
We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
We explore the possibilities for elementary embeddings $j : M \to N$, where $M$ and $N$ are models of ZFC with the same ordinals, $M \subseteq N$, and $N$ has access to large pieces of $j$. We construct commuting systems of such maps…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions ${\sf g}$ on ordinals is shown to be equal to the least fixed point of ${\sf g}$. Moreover corrections to the previous paper are made.
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…