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

Stratified Labelings for Abstract Argumentation

We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions

A Tree Logic with Graded Paths and Nominals

Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node cardinality constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential time

Understanding Social Investment Policy: evidence from the evaluation of Futurebuilders in England

The concept of social investment has attracted interest from policy makers, financial markets and not for profit organisations. It is an emergent notion which is multi-faceted and includes different market forms, policy responses, and institutional configurations. There is relatively little empirical evidence on the design, implementation and impacts of the various initiatives which have been perceived as falling within the field of social investment. This paper begins to address this gap. It draws on the national evaluation of Futurebuilders in England which was undertaken between 2005 and 2010. At the time Futurebuilders was one of the largest examples of a public policy initiative to support social investment; based on a policy model of government seeking to promote the use of loan funding to third sector organisations as part of a wider agenda of expanding the sector's role in the delivery of public services. The paper explores the effects of the programme on the third sector, on public service delivery and on service users. In conclusion the paper challenges some of the assumptions of this policy model, as well as the potential for 'impact investing' to become a framework for welfare provision

Strong Completeness of Coalgebraic Modal Logics

Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties - up to the point that canonical models may fail to exist, as is the case e.g. in most probabilistic logics. Here, we present a generic canonical model construction in the semantic framework of coalgebraic modal logic, which pinpoints coherence conditions between syntax and semantics of modal logics that guarantee strong completeness. We apply this method to reconstruct canonical model theorems that are either known or folklore, and moreover instantiate our method to obtain new strong completeness results. In particular, we prove strong completeness of graded modal logic with finite multiplicities, and of the modal logic of exact probabilities

Typicality, graded membership, and vagueness

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Education today: 12 + 5 < 4 - lessons of education reforms in Portugal and beyond

Since the adoption of the ‘Lei de Bases…’ of 1984, the quality of education in Portugal is declining, undermined by ‘critical, creative and independent thinking’, implemented by neglecting memorization as a learning tool, as supposedly students should understand things without knowing them. As a consequence, vast majority of students can’t retain any abstract knowledge. They prepare from scratch for their tests and forget everything afterwards. The students never acquire essential primary-school skills such as capacity to do mental calculations, hence the title of this report, comparing contemporary school + university education to pre-1984 primary school of 4 years. The quality of education is further degraded by ‘evaluation’ of teachers at school and university, judged by academic success and degree of satisfaction of their students. With the students objectively incapable to learn, understand or remember, the teachers have a dilemma of either letting such students pass without retained knowledge, skills and competences, or else have their own ‘evaluation’ suffer. As the generations change, students who were ‘passed’ become teachers themselves, still with no retained knowledge and thus no moral authority to fail their own students. Thus, the level of requirements monotonously degrades, with the educational fraud perpetuated in the new generations.info:eu-repo/semantics/publishedVersio