Related papers: Generic partiality for $\frac{3}{2}$-institutions
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
We introduce a notion of normalised oplax $3$-functor suitable for the elementary homotopy theory of strict $3$-categories, following the combinatorics of orientals. We show that any such morphism induces a morphism of simplicial sets…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
The extremization of an appropriate entropic functional may yield to the probability distribution functions maximizing the respective entropic structure. This procedure is known in Statistical Mechanics and Information Theory as Jaynes'…
The state complexity of the result of a regular operation is often positively correlated with the number of distinct transformations induced by letters in the minimal deterministic finite automaton of the input languages. That is, more…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…
It is well-known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current…
MacMahon showed that the generating function for partitions into at most $k$ parts can be decomposed into a partial fractions-type sum indexed by the partitions of $k$. In this present work, a generalization of MacMahon's result is given,…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…
This article is the last of the series of articles where we reprove the foundational ideas of abstract six-functor formalisms developed by Liu-Zheng. We prove the theorem of partial adjoints, which is a simplicial technique of encoding…
One of the problems of formal verification is that it is not functionally complete due the incompleteness of specifications. An implementation meeting an incomplete specification may still have a lot of bugs. In testing, this issue is…
We present a metagrammatical formalism, {\em generic rules}, to give a default interpretation to grammar rules. Our formalism introduces a process of {\em dynamic binding} interfacing the level of pure grammatical knowledge representation…
Institutions play a critical role in enabling communities to manage common-pool resources and avert tragedies of the commons. However, a fundamental issue arises: Individuals typically perceive participation as advantageous only after an…