Related papers: Continuous logic and the strict order property
A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce…
It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the…
In this paper we show that states, transitions and behavior of concurrent systems can often be modeled as sheaves over a suitable topological space. In this context, geometric logic can be used to describe which local properties (i.e.…
We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…
Opial's Lemma is a fundamental result in the convergence analysis of sequences generated by optimization algorithms in real Hilbert spaces. We introduce the concept of Opial sequences - sequences for which the limit of the distance to each…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Extending a theorem of Shelah we prove that fundamental groups of Peano continua (locally connected and connected metric compact spaces) are finitely presented if they are countable. The proof uses ideas from geometric group theory.
This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
We provide a short proof of Shelah's eventual categoricity conjecture, assuming the Generalized Continuum Hypothesis ($GCH$), for abstract elementary classes (AEC's) with interpolation, a strengthening of amalgamation which is a necessary…
We consider discrete-time uncertain processes with finite state space and study the properties of game-theoretic upper expectations developed by Shafer and Vovk. We start by proving some basic properties, e.g. monotonicity, law of iterated…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
This paper is a continuation of work started in \cite{njampavcont} on preserving continuity in ideal topological spaces. We will deal with $\theta$-continuity and weak continuity and give their translations in ideal topological spaces. As…
We introduce a new kind of infinitary logic that we call Boolean expansion of ${\mathcal L}_{\kappa \kappa}$. This logic involves a new kind of variable, that we call generalised Boolean variable. These variables range over the powerset of…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
This paper suggests a [email protected] of composable specification of concurrent programs that permits: (1) verification of program code for a given specification, and (2) composition of the specifications of the components to yield…