Pointwise intersection in neighbourhood modal logic

We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets $\mathcal{N}_i$ (one for each member $i$ of a set $G$, used to interpret the modality $\square_i$) to a new neighbourhood set $\mathcal{N}_G$, which in turn allows us to interpret the operator $\square_G$. Here, $X$ is in the neighbourhood for $G$ if and only if $X$ equals the intersection of some $\mathcal{Y} = \{Y_i \mid i\in G\}$. We show that the notion of pointwise intersection has various applications in epistemic and doxastic logic, deontic logic, coalition logic, and evidence logic. We then establish sound and strongly complete axiomatizations for the weakest logic characterized by pointwise intersection and for a number of variants, using a new and generally applicable technique for canonical model construction.Comment: Submitted to Advances in Modal Logic 201

PSPACE Bounds for Rank-1 Modal Logics

For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank-1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACE-bounds for a number of logics including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generic algorithm moreover finds tableau proofs that witness pleasant proof-theoretic properties including a weak subformula property. This generality is made possible by a coalgebraic semantics, which conveniently abstracts from the details of a given model class and thus allows covering a broad range of logics in a uniform way

Named Models in Coalgebraic Hybrid Logic

Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding

Exploring the relationship between land-use system and travel behaviour - some first findings

Theories on the reciprocal relationship between land-use and transport address changes in locational decisions and travel behavior of private actors (households and firms) due to alternations in the transport system, respectively land-use system. Although the impact of land-use system on travel behaviour (transport system) has been the subject of much research (for reviews, see, e.g. Handy, 2002; Stead and Marshall, 2001; Crane, 2000; Wegener and Fürst, 1999), there is still no consensus about the strength of this relationship. This may be caused by different types of variables whether or not included in the research. Initially only land-use variables were taken into account, but nowadays socio-economical variables are also incorporated. Still, within ‘homogeneous groups’, there may be attitudes, lifestyles, perceptions, and preferences which can have an impact on land-use and/or travel behaviour. Academic literature on the latter remains scarce and the main focus of the existing behavioural literature is the impact of residential location on travel choices, especially modal choice. However, little work has thus far been done on other dimensions of travel choices (e.g., distance, time) and other location types (e.g., commercial, industrial, recreational). Less is known about the reverse relationship, e.g. the impact of the transport system on location decisions of households and firms (land-use system). A difference in time-scale can be the reason for this. Transformations in land-use occur much slower (years) compared to transformations in travel behaviour (days, weeks, months). In this paper we explore several possibilities to fill in some of the gaps in our knowledge on the land-use/transport system. Understanding the two-way interaction between land-use and travel behaviour involves having (i) data on land-use patterns, socio-economic background of individuals and their attitudes, perceptions and preferences towards land-use and travel; and (ii) a methodology, dealing with potential multiple directions of causality. The first issue can be achieved by combining empirical, revealed and stated preference research. The second methodological question can be solved using structural equation modelling (SEM). This is a modelling technique which can handle a large number of endogenous and exogenous variables. Because of the multiple directions of causality that can be explored, SEM can help us to define the relationship between revealed preference data and stated preference data.