The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable. The decidability of the finite satisfiability problem of two-variable logic extended by orders and preorders as well as their corresponding successor relations has been currently investigated by several papers [2, 5, 3]. This short note extends [3] wh...

We implement belief revision in SNePS based on a user-supplied epistemic ordering of propositions. We provide a decision procedure that performs revision completely automatically when given a well preorder. We also provide a decision procedure for revision that, when given a total preorder, simulates a well preorder by making a minimal number of queries to the user when multiple propositions wi...

This paper proposes a way to effectively compare the potential of processes to cause conflict. In discrete event systems theory, two concurrent systems are said to be in conflict if they can get trapped in a situation where they are both waiting or running endlessly, forever unable to complete their common task. The conflict preorder is a process-algebraic pre-congruence that compares two proce...

In the standard testing theory of DeNicola-Hennessy one process is considered to be a refinement of another if every test guaranteed by the former is also guaranteed by the latter. In the domain of web services this has been recast, with processes viewed as servers and tests as clients. In this way the standard refinement preorder between servers is determined by their ability to satisfy client...

In this paper we consider Milner's calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We deene operational notions of preorder and equivalence as prob-abilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...

The uniform verification problem for parameterized systems is to determine whether a temporal property is true for every instance of the system which is composed of an arbitrary number of homogeneous processes. We consider some aspects of the inductionbased technique which assumes the construction of finite invariants of such systems. An invariant process is one which is greater (with respect t...

We present some sufficient conditions for the existence of a continuous multi-utility representation of a preorder on a topological space (X, τ) (i.e., for the existence of a family F of continuous increasing realvalued functions on the preordered topological space (X, τ, ) such that, for every pair of elements (x, y) ∈ X×X, x y ⇔ f(x) ≤ f(y) ∀f ∈ F). Such conditions are based on the concept of...

An inequality preorder is defined as a complete preorder on a simplex which satisfies the properties of continuity and strict Schur-convexity (the mathematical equivalent of Dalton's "principle of transfers"). The paper shows that it is possible to aggregate individual inequality preorders into a collective one if we are interested in continuous anonymous aggregation rules that respect unanimit...

The finite satisfiability problem for two-variable logic over structures with unary relations and two order relations is investigated. Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically, we show that this problem is complete for EXPSPACE. As a consequence, the same upper bound applies to the case of two linear orders. ...

This work presents a minimization algorithm. The algorithm receives a Kripke structure M and returns the smallest structure that is simulation equivalent to M. The simulation equivalencerelation is weaker than bisimulation but stronger than the simulation preorder. It strongly preserves ACTL and LTL (as sub-logics of ACTL). We show that every structure M has a unique up to isomorphism reduced s...