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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…
Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which…
In a recent letter [Information Processing Letters~104 (2007) 152-158], it has shown some sufficient conditions for commutativity of quantum weakest preconditions. This paper provides some alternative and simple characterizations for the…
An equational condition is a set of equations in an algebraic language, and an algebraic structure satisfies such a condition if it possesses terms that meet the required equations. We find a single nontrivial equational condition which is…
We present a semantics of a probabilistic while-language with soft conditioning and continuous distributions which handles programs diverging with positive probability. To this end, we extend the probabilistic guarded command language…
This paper discusses the existence of a sufficient condition for an operator to be weakly hypercyclic. We establish a weak hypercyclicity criterion, and thereupon we can answer questions 5.3 and 5.8 posed by Chan and Sanders in 2004.…
This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving…
The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of 'strong equivalence' between logical programs that can be verified in 3-valued Goedel logic, G3,…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally distinct. To establish this, we introduce left…
Liveness properties, such as termination, of even the simplest shared-memory concurrent programs under sequential consistency typically require some fairness assumptions about the scheduler. Under weak memory models, we observe that the…
Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
Context: Conditional statements like "If A and B then C" are core elements for describing software requirements. However, there are many ways to express such conditionals in natural language and also many ways how they can be interpreted.…
We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term $L_\infty$-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big…
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic…
Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework,…
This paper maps out the relation between different approaches for handling preferences in argumentation with strict rules and defeasible assumptions by offering translations between them. The systems we compare are: non-prioritized defeats…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…