Related papers: Bisimulation for Impure Simplicial Complexes
We study structural and enumerative aspects of pure simplicial complexes and clique complexes. We prove a necessary and sufficient condition for any simplicial complex to be a clique complex that depends only on the list of facets. We also…
We describe software and a language for quasibiological computations. Its theoretical basis is a unified theory of complex (adaptive) systems where all laws are regularities of relations between things or agents, and dynamics is made from…
An abstract simplicial complex is said to be $d$-representable if it records the intersection pattern of a collection of convex sets in $\mathbb{R}^d$. In this paper, we show that $d$-representability of a simplicial complex is equivalent…
There is an apparent similarity between the descriptions of small-step operational semantics of imperative programs and the semantics of finite automata, so defining an abstraction mapping from semantics to automata and proving a simulation…
We provide a novel semantics for belief using simplicial complexes. In our framework, belief satisfies the \textsf{KD45} axioms and rules as well as the ``knowledge implies belief'' axiom ($K\phi \lthen B\phi$); in addition, we adopt the…
In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish…
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer…
In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, \rho), where Q is a word in the alphabet of simple reflections, \rho is a group element. We describe the transformations of such a complex…
An epistemic ensemble is composed of knowledge-based agents capable of retrieving and sharing knowledge and beliefs about themselves and their peers. These agents access a global knowledge state and use actions to communicate and cooperate,…
Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…
Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of…
Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…
Let $G$ be a finite group. In 2024, Cameron introduced two different concepts of independence (namely independence and strong independence) for the subsets of $G$, yielding to the definition of two simplicial complexes whose vertices are…
We introduce higher simplicial complexity of a simplicial complex $K$ and higher combinatorial complexity of a finite space $P$ (i.e. $P$ is a finite poset). We relate higher simplicial complexity with higher topological complexity of $|K|$…
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such…
A persistent challenge in practical classification tasks is that labeled training sets are not always available. In particle physics, this challenge is surmounted by the use of simulations. These simulations accurately reproduce most…
Let X,Y be finite sets and T a set of functions from X -> Y which we will call "tableaux". We define a simplicial complex whose facets, all of the same dimension, correspond to these tableaux. Such "tableau complexes" have many nice…