In this article I try to investigate the possible insights one may reach by considering the development on the level of socio-philosophical theories as a symptom of the development taking place on the level of social practice.

We explore the finite model theory of the characterisation theorems for modal and guarded fragments of first-order logic over transition systems and relational structures of width two. A new construction of locally acyclic bisimilar covers provides a useful analogue of the well known tree-like unravellings that can be used for the purposes of finite model theory. Together with various other finitary bisimulation respecting model transformations, and Ehrenfeucht–Fraïssé game arguments, these covers allow us to upgrade finite approximations for full bisimulation equivalence (...) towards approximations for elementary equivalence. These techniques are used to prove several ramifications of the van Benthem–Rosen characterisation theorem of basic modal logic for refinements of ordinary bisimulation equivalence, both in the sense of classical and of finite model theory. (shrink)

We investigate model theoretic characterisations of the expressive power of modal logics in terms of bisimulation invariance. The paradigmatic result of this kind is van Benthem’s theorem, which says that a first-order formula is invariant under bisimulation if, and only if, it is equivalent to a formula of basic modal logic. The present investigation primarily concerns ramifications for specific classes of structures. We study in particular model classes defined through conditions on the underlying frames, with a focus on frame classes (...) that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics. Classical model theoretic arguments do not apply to many of the most interesting classes–for instance, rooted frames, finite rooted frames, finite transitive frames, well-founded transitive frames, finite equivalence frames–as these are not elementary. Instead we develop and extend the game-based analysis over such classes and provide bisimulation preserving model constructions within these classes. Over most of the classes considered, we obtain finite model theory analogues of the classically expected characterisations, with new proofs also for the classical setting. The class of transitive frames is a notable exception, with a marked difference between the classical and the finite model theory of bisimulation invariant first-order properties. Over the class of all finite transitive frames in particular, we find that monadic second-order logic is no more expressive than first-order as far as bisimulation invariant properties are concerned — though both are more expressive here than basic modal logic. We obtain ramifications of the de Jongh–Sambin theorem and a new and specific analogue of the Janin–Walukiewicz characterisation of bisimulation invariant monadic second-order for finite transitive frames. (shrink)

How can we prove that some fragment of a given logic has the power to define precisely all structural properties that satisfy some characteristic semantic preservation condition? This issue is a fundamental one for classical model theory and applications in non-classical settings alike. While methods differ greatly, and while the classical methods can usually not be matched for instance in the setting of finite model theory, this note surveys some interesting commonality revolving around the use and availability of tractable representatives (...) in the relevant model classes. The construction of models in which simple invariants like partial types based on some weak fragment control all the relevant structural properties, may be seen at the heart of such questions. We highlight some constructions involving degrees of acyclicity and saturation that can be achieved in finite model constructions, and discuss their uses towards expressive completeness w.r.t. bisimulation based equivalences in hypergraphs and relational structures. The emphasis is on the combinatorial challenges in such more constructive approaches that work in non-classical settings and especially in finite model theory. One new result concerns expressive completeness w.r.t. guarded negation bisimulation, a back-and-forth equivalence involving local homomorphisms. (shrink)

The satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively wellordered, domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems is essentially (...) the same as for plain unconstrained FO 2 , namely non-deterministic exponential time. In contrast FO 2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings, wellorderings, or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO 2 and computation tree logic CTL. (shrink)

We study the expressive power in the finite of the logic Fixed-Point+Counting, the extension of first-order logic which is obtained through adding both the fixed-point constructor and the ability to count. To this end an isomorphism preserving (`generic') model of computation is introduced whose PTime restriction exactly corresponds to this level of expressive power, while its PSpace restriction corresponds to While+Counting. From this model we obtain a normal form which shows a rather clear separation of the relational vs. the arithmetical (...) side of the algorithms involved. In parallel, we study the relations of Fixed-Point+Counting with the infinitary logics L r ∞ω (∃ ≥ m ) m∈ω and the corresponding pebble games. The main result, however, involves the concept of an arithmetical invariant. By this we mean a functor taking every finite relational structure to an expansion of (an initial segment of) the standard arithmetical structure. In particular its values are linearly ordered structures. We establish the existence of a family of arithmetical invariants (J r ) r≥ 1 with the following properties: $\bullet$ The invariants themselves can be evaluated in polynomial time. $\bullet$ A class of finite relational structures is definable in Fixed-Point+Counting if and only if membership can be decided in polynomial time on the basis of the values of one of the invariants. $\bullet$ The invariant J r classifies all finite relational structures exactly up to equivalence with respect to the logic L r ∞ω (∃ ≥ m ) m∈ω . We also give a characterization of Fixed-Point+Counting in terms of sequences of formulae in the L r ωω (∃ ≥ m ) m∈ω : It corresponds exactly to the polynomial time computable families (φ n ) n∈ω in these logics. Towards a positive assessment of the expressive power of Fixed-Point+Counting, it is shown that the natural extension of fixed-point logic by Lindström quantifiers, which capture all the PTime computable properties of cardinalities of definable predicates, is strictly weaker than what we get here. This implies in particular that every extension of fixed-point logic by means of monadic Lindstrom quantifiers, which stays within PTime, must be strictly contained in Fixed-Point+Counting. (shrink)

Lyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of first-order logic, there is an interpolant in which each relation symbol appears positively (negatively) only if it appears positively (negatively) in both the antecedent and the succedent of the given implication. We prove a similar, more general interpolation result with the additional requirement that, for some fixed tuple U of unary predicates U, all formulae under consideration have all quantifiers explicitly relativised to one of the (...) U. Under this stipulation, existential (universal) quantification over U contributes a positive (negative) occurrence of U. It is shown how this single new interpolation theorem, obtained by a canonical and rather elementary model theoretic proof, unifies a number of related results: the classical characterisation theorems concerning extensions (substructures) with those concerning monotonicity, as well as a many-sorted interpolation theorem focusing on positive vs. negative occurrences of predicates and on existentially vs. universally quantified sorts. (shrink)

We consider infinitary logic with only two variable symbols, both with and without counting quantifiers, i.e. L2 L∞ω2 and C2 L∞ω2mεω. The main result is that finite relational structures admit canonization with respect to L2 and C2: there are polynomial time com putable functors mapping finite relational structures to unique representatives of their equivalence class with respect to indistinguishability in either of these logics. In fact we exhibit in verses to the natural invariants that characterize structures up to L2- or (...) C2-equivalence, respectively. As a corollary we obtain recursive presentations of the classes of all boolean queries that are closed with respect to L2- or C2-equivalence. (shrink)

There are properties of finite structures that are expressible with the use of Hilbert's ε-operator in a manner that does not depend on the actual interpretation for ε-terms, but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in first-order logic over finite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power of first-order logic (...) even as far as deterministic queries are concerned, thereby answering a question raised by Abiteboul and Vianu. (shrink)

By means of an Ehrenfeucht-Mostowski construction we obtain an automorphism theorem for a syntactically characterized class of Laa-theories comprising in particular the finitely determinate ones. Examples of Laa-theories with only rigid models show this result to be optimal with respect to a classification in terms of prenex quantifier type: Rigidity is seen to hinge on quantification of type $\ldots\forall\ldots\mathbf{\operatorname{stat}}\ldots$ permitting of the parametrization of families of disjoint stationary systems by the elements of the universe.

We consider a class of Lindström extensions of first-order logic which are susceptible to a natural Skolemization procedure. In these logics Ehrenfeucht Mostowski (EM) functors for theories with arbitrarily large models can be obtained under suitable restrictions. Characteristic dependencies between algebraic properties of the quantifiers and the maximal domains of EM functors are investigated.Results are applied to Magidor Malitz logic,L(Q <ω), showing e.g. its Hanf number to be equal to ℶω(ℵ1) in the countably compact case. Using results of Baumgartner, the (...) maximal number of isomorphism types of linearly ordered models of regular cardinality is shown to be achieved for theories that admit an EM functor on a typically restricted domain. (shrink)

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate (...) the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. (shrink)

It is a classical result of Mortimer that $L^2$ , first-order logic with two variables, is decidable for satisfiability. We show that going beyond $L^2$ by adding any one of the following leads to an undecidable logic:– very weak forms of recursion, viz.¶(i) transitive closure operations¶(ii) (restricted) monadic fixed-point operations¶– weak access to cardinalities, through the Härtig (or equicardinality) quantifier¶– a choice construct known as Hilbert's $\epsilon$ -operator.In fact all these extensions of $L^2$ prove to be undecidable both for satisfiability, (...) and for satisfiability in finite structures. Moreover most of them are hard for $\Sigma^1_1$ , the first level of the analytical hierachy, and thus have a much higher degree of undecidability than first-order logic. (shrink)

We study first-order logic with two variables FO² and establish a small substructure property. Similar to the small model property for FO² we obtain an exponential size bound on embedded substructures, relative to a fixed surrounding structure that may be infinite. We apply this technique to analyse the satisfiability problem for FO² under constraints that require several binary relations to be interpreted as equivalence relations. With a single equivalence relation, FO² has the finite model property and is complete for non-deterministic (...) exponential time, just as for plain FO² With two equivalence relations, FO² does not have the finite model property, but is shown to be decidable via a construction of regular models that admit finite descriptions even though they may necessarily be infinite. For three or more equivalence relations, FO² is undecidable. (shrink)

We present a natural standard translation of inquisitive modal logic $\mathrm{InqML}$ into first-order logic over the natural two-sorted relational representations of the intended models, which captures the built-in higher-order features of $\mathrm{InqML}$. This translation is based on a graded notion of flatness that ties the inherent second-order, team-semantic features of $\mathrm{InqML}$ over information states to subsets or tuples of bounded size. A natural notion of pseudo-models, which relaxes the non-elementary constraints on the intended models, gives rise to an elementary, purely (...) model-theoretic proof of the compactness property for $\mathrm{InqML}$. Moreover, we prove a Hennessy-Milner theorem for $\mathrm{InqML}$, which crucially uses $\omega $ -saturated pseudo-models and the new standard translation. As corollaries we also obtain van Benthem style characterisation theorems. (shrink)

We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques-thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms (...) of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF. (shrink)

Consider the bounded variable logics $L^k_{\infty\omega}$ (with k variable symbols), and $C^k_{\infty\omega}$ (with k variables in the presence of counting quantifiers $\exists^{\geq m}$ ). These fragments of infinitary logic $L_{\infty\omega}$ are well known to provide an adequate logical framework for some important issues in finite model theory. This paper deals with a translation that associates equivalence of structures in the k-variable fragments with bisimulation equivalence between derived structures. Apart from a uniform and intuitively appealing treatment of these equivalences, this approach (...) relates some interesting issues for the case of an arbitrary number of variables to the case of just three variables. Invertibility of the invariants for $\equiv_{C^3}$ , in particular, would imply a positive answer to the tempting conjecture that fixed-point logic with counting captures $\bigcup_k$ Ptime $\cap C^k_{\infty\omega}$. (shrink)

Entrepreneurship education is increasingly becoming a focal strategy for promoting entrepreneurship, particularly to foster entrepreneurial intentions and startups. However, learning and support are equally important after startup for novice entrepreneurs to gain a good level of confidence to manage their business and achieve the desired outcomes. Using a sample of 189 young self-employed individuals in Uganda, this study examines the differential impact of mentoring and self-efficacy on the achievement of intangible outcomes of entrepreneurship including satisfaction of need for autonomy, work (...) satisfaction and the intention to stay in self-employment. We found self-efficacy to mediate the effects of mentoring on these intangible outcomes. In addition, the results showed substantial gender differences. Whereas women’s satisfaction of the need for autonomy and intention to stay in self-employment were strongly associated with the direct effects of mentoring, their male counterparts seemed to benefit more if mentoring resulted in increased self-efficacy. Overall, our findings suggest that whereas mentoring improves the competence of small business owners and consequently achievement of superior outcomes, mentoring should also focus on boosting self-efficacy which in turn is essential for the application of the entrepreneurial competencies. (shrink)

Recent research illustrates substantial gaps between entrepreneurial intentions and behavior. This is a challenge for entrepreneurship promotion interventions that have primarily focused on stimulating entrepreneurial intentions. However, extant literature suggests that implementation intentions enhance the likelihood of acting congruently to the behavioral intention. Furthermore, theory also suggests the condition effects of situations and the perceived control over them. We therefore hypothesized that implementation intentions mediate the relationship between entrepreneurial intention and action, while perceived family support moderates the movement from implementation (...) intention to entrepreneurial action. Using two-wave survey data from a sample of students at an African university, we measured two psychological attributes as important precursors of entrepreneurship and entrepreneurial intentions present before undertaking an innovations and entrepreneurship course. Implementation intentions regarding entrepreneurship, entrepreneurial actions, and perceived parental support for entrepreneurial activities were also measured 2 weeks after completion of the course. Our results demonstrate support for the proposed moderated double mediation model in which the effects of the two psychological attributes on entrepreneurial actions are explained via entrepreneurial intentions and implementation intentions. We further find moderation effects of perceived family support indicating that implementation intentions more likely predicted entrepreneurial actions in cases of higher family support. (shrink)

This inclusive cross-cultural study rethinks the nexus between engineering education and context. In so doing the book offers a reflection on contextual boundaries with an overall boundary crossing ambition and juxtaposes important cases of critical participation within engineering education with sophisticated scholarly reflection on both opportunities and discontents. Whether, and in what way engineering education is or ought to be contextualized or de-contextualized is an object of heated debate among engineering educators. The uniqueness of this study is that this debate (...) is given comprehensive coverage - presenting both instrumentally inclined as well as radical positions on transforming engineering education. In contextualizing engineering education, this book offers diverse commentary from a range of disciplinary, meta- and interdisciplinary perspectives on how cultural, professional, institutional, and educational systems contexts shape histories, structural dynamics, ideologies and challenges as well as new pathways in engineering education. Topics addressed include examining engineering education in countries ranging from India to America, to racial and gender equity in engineering education and incorporating social awareness into the area. Using context as "bridge" this book confronts engineering education head on. Contending engineering ideologies and corresponding views on context are juxtaposed with contending discourses of reform. The uniqueness of the book is that it brings together scholars from the humanities, the social sciences and engineering from Europe - both East and West - with the United States, China, Brazil, India and Australia. (shrink)

The interaction between American pragmatism and German critical theory has a long history. While Horkheimer and Adorno, the founding fathers of critical theory, were quite critical of the native American philosophy they encountered when they fled from Nazi Germany, American pragmatism has had a considerable influence on both Jürgen Habermas and Axel Honneth—the two most prominent thinkers within critical theory’s 2nd and 3rd generations. As is well known, however, their prime inspiration has been George Herbert Mead’s symbolic interactionist sociology as (...) well as Peirce’s theory of signs, while James’ and Dewey’s thinking has played a minor role for them. However, in Axel Honneth’s most recent book, The idea of... (shrink)

This paper examines the way in which Ordinary Language Philosophy came to exert an important influence on the work done at Aarhus University’s department of philosophy in the latter half of the 20th century. The first section depicts the rise of Ordinary Language Philosophy as an international movement centered around Oxford in the wake of World War ii. The second section goes on to describe how it was brought to Aarhus by Professor Justus Hartnack, who had been deeply influenced by (...) the movement during stays abroad in the UK and the US. The following three sections move on to describe some of the important ways in which Ordinary Language Philosophy has influenced the work of three of Hartnack’s most prominent students, who have influenced the life of the department in crucial ways from the 1970s until recently. Finally, the paper ends by briefly assessing the legacy and contemporary influence of Ordinary Language Philosophy in Aarhus. (shrink)

Much research has been done on the economic effects of self-employment, environmental conditions for entrepreneurial success, as well as attributes if the person him-/herself fits to this career path. To successfully run a business, however, is contingent on the health of the entrepreneur. In particular, small business owners (being solo self-employed without personnel) face financial uncertainties, a high workload, long working hours, and are often unable to call in sick. This study aimed at exploring the working situation considering resources (e.g., (...) autonomy), strain (e.g., dependency on contracts with clients) and health and career outcomes of small business owners. This study used a qualitative approach to comprehensively mirror the working situation. Participants who were 29 small business owners from Germany gave permission for recording expert interviews in which they reported, for example, on health complaints, recovery opportunities, obstacles and resources while running their businesses. The interviews emphasize the meaning of active actions and own responsibility for creating working conditions and enabling autonomy. Small business owners yet have to be able to use the autonomy. Besides personal preferences regarding the career path as being pulled into self-employment and not pushed by situational circumstances also marketability and flexibility played a role and explained health and career issues. Our findings underline that the social network is of utmost importance to small business owners and that social support – even or despite of being solo self-employed – is a key to sustaining health and satisfaction. As voluntariness played an essential role for selecting this specific career path those being pulled into self-employment as no other jobs are available should receive particular support through career counseling. One shortcoming of prior research is that the concrete working situation of small business owners and its impact on health and career has not adequately been taken into account. Based on work-related stress models we developed a frame model specific for the situation of small business owners which allows concrete hypotheses for further quantitative research. (shrink)

Fascinating and compelling in equal measure this volume presents a critical examination of the multilayered relationships between engineering and business. In so doing the study also stimulates ethical reflection on how these relationships either enhance or inhibit strategies to address vital issues of our time. In the context of geopolitical, economic, and environmental tendencies the authors explore the world that we should want to create and the role of the engineer and the business manager in this endeavor. Throughout this volume (...) the authors identify periods of alignment and periods of tension between engineering and business. They look at focal points of the engineering-business nexus related to the development of capitalism. The book explores past and present movements to reshape, reform, or reject this nexus. The volume is informed by questions of importance for industry as well as for higher education. These are: What kinds of conflict arise for engineers in their attempts to straddle both professional and organizational commitments? How should professionals be managed to avoid a clash of managerial and professional cultures? How do engineers create value in firms and corporations? What kinds of tension exist between higher education and industry? What challenges does the neoliberal entrepreneurial university pose for management, faculty, students, society, and industry? Should engineering graduates be ready for work, and can they possibly be? What kinds of business issues are reflected in engineering education curricula, and for what purpose? Is there a limit to the degree of business hybridization in engineering degree programs, and if so, what would be the criterion for its definition? Is there a place in engineering education curricula for reflective critique of assumptions related to business and economic thinking? One ideal of management and control comes to the fore as the Anthropocene - the world transformed into an engineered artefact which includes human existence. The volume raises the question as to how engineering and business together should be considered, given the fact that the current engineering-business nexus remains embedded within an economic model of continual growth. By addressing macro-level issues such as energy policy, sustainable development, globalization, and social justice this study will both help create awareness and stimulate development of self-knowledge among practitioners, educators, and students thereby ultimately addressing the need for better informed citizens to safeguard planet Earth as a human life supporting system. (shrink)

The editors discuss issues related to the journal, its editing process and publication model.

The editors discuss issues related to the journal, its editing process and publication model.

The editors discuss issues related to the journal, its editing process and publication model.

This second companion volume on engineering studies considers engineering practice including contextual analyses of engineering identity, epistemologies and values. Key overlapping questions examine such issues as an engineering identity, engineering self-understandings enacted in the professional world, distinctive characters of engineering knowledge and how engineering science and engineering design interact in practice. -/- Authors bring with them perspectives from their institutional homes in Europe, North America, Australia\ and Asia. The volume includes 24 contributions by more than 30 authors from engineering, the (...) social sciences and the humanities. Additional issues the chapters scrutinize include prominent norms of engineering, how they interact with the values of efficiency or environmental sustainability. A concluding set of articles considers the meaning of context more generally by asking if engineers create their own contexts or are they created by contexts. -/- Taken as a whole, this collection of original scholarly work is unique in its broad, multidisciplinary consideration of the changing character of engineering practice. (shrink)

Although the body of literature in sport science is growing rapidly, certain sports have yet to benefit from this increased interest by the scientific community. One such sport is Ultimate Frisbee, officially known as Ultimate. Thus, the goal of this study was to describe the nature of the sport by identifying differences between winning and losing teams in elite-level competition. To do so, a customized observational system and a state transition model were developed and applied to 14 games from the (...) 2017 American Ultimate Disc League season. The results reveal that, on average, 262.2 passes were completed by a team per game and 5.5 passes per possession. More than two-thirds of these passes were played from the mid zone and the rear zone, nearest the team’s own end zone. Winning and losing teams do not differ in these general patterns, but winning teams played significantly fewer backward passes from the front zone to the mid zone, nearest the opponent’s end zone than losing teams = −4.980, p < 0.001, d = −1.16). Furthermore, losing teams scored fewer points when they started on defense, called breakpoints = −6.365, p < 0.001, d = 2.30), and committed significantly more turnovers per game = 5.85, p < 0.001, d = −1.18). Overall, this study provides the first empirical description of Ultimate and identifies relevant performance indicators to discriminate between winning and losing teams. We hope this article sheds light on the unique, but so far overlooked sport of Ultimate, and offers performance analysts the basis for future studies using state transition modeling in Ultimate as well as other invasion sports. (shrink)

This inclusive cross-cultural study rethinks the nexus between engineering education and context. In so doing the book offers a reflection on contextual boundaries with an overall boundary crossing ambition and juxtaposes important cases of critical participation within engineering education with sophisticated scholarly reflection on both opportunities and discontents. -/- Whether and in what way engineering education is or ought to be contextualized or de-contextualized is an object of heated debate among engineering educators. The uniqueness of this study is that this (...) debate is given comprehensive coverage – presenting both instrumentally inclined as well as radical positions on transforming engineering education. -/- In contextualizing engineering education, this book offers diverse commentary from a range of disciplinary, meta- and interdisciplinary perspectives on how cultural, professional, institutional and educational systems contexts shape histories, structural dynamics, ideologies and challenges as well as new pathways in engineering education. Topics addressed include examining engineering education in countries ranging from India to America, to racial and gender equity in engineering education and incorporating social awareness into the area. -/- Using context as “bridge” this book confronts engineering education head on. Contending engineering ideologies and corresponding views on context are juxtaposed with contending discourses of reform. The uniqueness of the book is that it brings together scholars from the humanities, the social sciences and engineering from Europe – both East and West – with the United States, China, Brazil, India and Australia. (shrink)