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A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers.…
We propose a conformity-driven reproductive ability in which an individual $i$ is more (less) likely to imitate a neighbor $j$'s strategy if $j$'s strategy is majority (minority) in $i$'s neighborhood. The results on the evolutionary…
We provide a constraint based computational model of linear precedence as employed in the HPSG grammar formalism. An extended feature logic which adds a wide range of constraints involving precedence is described. A sound, complete and…
The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this…
In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…
We study incompatibility of measurements and its relation to steering and nonlocality in a class of finite dimensional general probabilistic theories (GPT).The basic idea is to represent finite collections of measurements as affine maps of…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
The paper demonstrates that strict adherence to probability theory does not preclude the use of concurrent, self-activated constraint-propagation mechanisms for managing uncertainty. Maintaining local records of sources-of-belief allows…
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
We study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of…
Provability logics are modal or polymodal systems designed for modeling the behavior of G\"odel's provability predicate in arithmetical theories and its natural extensions. If \Lambda is any ordinal, the G\"odel-L\"ob calculus GLP(\Lambda)…
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…
This short squib looks at how using a broader definition of G\"odel numbering to mimic the accessibility relation between possible worlds results in two-world systems that sidestep undecidable sentences as well as the Liar paradox.
There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable.…
Distributive laws are important for algebraic reasoning in arithmetic and logic. They are equally important for algebraic reasoning about concurrent programs. In existing theories such as Concurrent Kleene Algebra, only partial correctness…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for…