Related papers: Algebraic Meta-Theory of Processes with Data
We present a unified rule format for structural operational semantics with terms as labels that guarantees that the associated labelled transition system has some bounded-nondeterminism property. The properties we consider include finite…
We give sound and complete axiomatizations for XPath with data tests by "equality" or "inequality", and containing the single "child" axis. This data-aware logic predicts over data trees, which are tree-like structures whose every node…
Conditions are essential in the statements of biological literature. Without the conditions (e.g., environment, equipment) that were precisely specified, the facts (e.g., observations) in the statements may no longer be valid. One…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
The graded affine Lie algebras provide a framework in which the dressing method is applied to the generic type of integrable models. The dressing formalism is used to develop a unified approach to various symmetry flows encountered among…
A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Context: Tables are ubiquitous formats for data. Therefore, techniques for writing correct programs over tables, and debugging incorrect ones, are vital. Our specific focus in this paper is on rich types that articulate the properties of…
We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the…
Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…
We derive an implicit description of the image of a semialgebraic set under a birational map, provided that the denominators of the map are positive on the set. For statistical models which are globally rationally identifiable, this yields…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpretation as homotopies in cell complexes. This has potential…
We present a straightforward, sound Hindley-Milner polymorphic type system for algebraic effects and handlers in a call-by-value calculus, which allows type variable generalisation of arbitrary computations, not just values. This result is…
Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are…
Accuracy-based evaluation cannot reliably distinguish genuine generalization from shortcuts like memorization, leakage, or brittle heuristics, especially in small-data regimes. In this position paper, we argue for mechanism-aware evaluation…
We concentrate our study on a recent process algebra - PALOMA - intended to capture interactions between spatially distributed agents, for example in collective adaptive systems. New agent-based semantic rules for deriving the underlying…