74 research outputs found

### Bisimulation for Weakly Expressive Coalgebraic Modal Logics

Research on the expressiveness of coalgebraic modal logics with respect to semantic equivalence notions has so far focused mainly on finding logics that are able to distinguish states that are not behaviourally equivalent (such logics are said to be expressive). In other words, the notion of behavioural equivalence is taken as the starting point, and the expressiveness of the logic is evaluated against it. However, for some applications, modal logics that are not expressive are of independent interest. Such an example is given by contingency logic. We can now turn the question of expressiveness around and ask, given a modal logic, what is a suitable notion of semantic equivalence? In this paper, we propose a notion of Lambda-bisimulation which is parametric in a collection Lambda of predicate liftings. We study the basic properties of Lambda-bisimilarity, and prove as our main result a Hennessy-Milner style theorem, which shows that (for finitary functors) Lambda-bisimilarity exactly matches the expressiveness of the coalgebraic modal logic arising from Lambda

### Presenting Distributive Laws

Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages

### A (Co)algebraic Approach to Hennessy-Milner Theorems for Weakly Expressive Logics

Coalgebraic modal logic, as in [9, 6], is a framework in which modal logics for specifying coalgebras can be developed parametric in the signature of the modal language and the coalgebra type functor T. Given a base logic (usually classical propositional logic), modalities are interpreted via so-called predicate liftings for the functor T. These are natural transformations that turn a predicate over the state space X into a predicate over TX. Given that T-coalgebras come with general notions of T-bisimilarity [11] and behavioral equivalence [7], coalgebraic modal logics are designed to respect those. In particular, if two states are behaviourally equivalent then they satisfy the same formulas. If the converse holds, then the logic is said to be expressive. and we have a generalisation of the classic Hennessy-Milner theorem [5] which states that over the class of image-fjnite Kripke models, two states are Kripke bisimilar if and only if they satisfy the same formulas in Hennessy-Milner logic

### An agent-based exploration of the effect of multi-criteria decisions on complex socio-technical heat transitions

Natural gas for heating is widespread in the built environment of The Netherlands, where the government aims at limiting heat demand and reducing natural gas consumption over the coming decades. In the owner-occupied residential sector, this transition is complex and requires cooperation and coordination of individuals and groups that make investment decisions. We use agent-based modelling to explore the effect that various financial policies could have in an illustrative neighbourhood, given that households make multi-criteria and group decisions. In the scientific literature, this type of energy model seldom focuses on the adoption of competing technologies by households as individual and collective agents grouped in homeowner associations in multi-family buildings. To address the problem and knowledge gaps, we model individual preferences with a multi-criteria perceived lifetime utility submodel, and decisions as outcomes of individual preferences and a threshold voting system. We explore energy taxes (natural gas and electricity), regulated price of heat from networks, and subsidies (insulation and heat pumps). Under our assumptions, we found that combinations of fiscal policies, regulated heat prices, and subsidies can sometimes create incentives for households to disconnect from natural gas, but that steering the transition mainly with financial policies could prove ineffective. We also found that, in terms of collective CO2 reduction, some transitions in which only some households phase out natural gas could have results similar to some scenarios in which households only improve their dwellingsâ€™ insulation levels

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