Abstract
Abstract We introduce a substructural modal logic of utility that can be used to reason aboutoptimality with respect to properties of states. Our notion of state is quite general, and is able to represent resource allocation problems in distributed systems. The underlying logic is a variant of the modal logic of bunched implications, and based on resource semantics, which is closely related to concurrent separation logic. We consider a labelled transition semantics and establish conditions under which Hennessy—Milner soundness and completeness hold. By considering notions of cost, strategy and utility, we are able to formulate characterizations of Pareto optimality, best responses, and Nash equilibrium within resource semantics. We also show that our logic is able to serve as a logic for a fully featured process algebra and explain the interaction between utility and the structure of processes.
Highlights
Mathematical modelling and simulation modelling are fundamental tools of engineering, science and social sciences such as economics, and provide decision-support tools in management
We develop a substructural modal predicate logic, MBIU, that can be used to reason about optimality with respect to properties of states
We employ an abstract formulation of MBIU that is based on a semantics that employs a labelled transition system, a notion of concurrent composition of states, and an equivalence relation on actions
Summary
Mathematical modelling and simulation modelling are fundamental tools of engineering, science and social sciences such as economics, and provide decision-support tools in management. We must we introduce actions, and define a notion of transition systems with concurrent structure on their states. We introduce a slight variant on the standard notion of bisimulation for such a transition system, and describe various properties that we require for our results to hold; in particular, that the concurrent composition operator is a congruence with respect to the bisimulation relation. In a given starting state, makes a choice between possible actions and so evolves, along with its environment, to achieve a new state Associated with such an action is its value, or utility, which is determined by a payoff function. In order to define MBIU, we must introduce actions on states, their transition systems and the associated notion of bisimulation, payoffs, and strategies. A short version of this article is [1]
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