Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation of (...) inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is (...) removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

This article investigates the naturalisation of the Bible. Three voices are of special importance in the narrative presented in this article; they are Aristotle, Rene Descartes and Baruc Spinoza. This article will investigate the scientific method and metaphysics espoused by each of the three scholars, thereby highlighting changes in scientific method and metaphysics that lead to the naturalisation of the Bible. Firstly, Aristotle pioneered a scientific method that would dominate for centuries, as well as a highly influential metaphysics. Secondly, Descartes, (...) witnessing the horrors of the Thirty Years War and seeing first-hand the new discoveries that brought about the scientific revolution, reacted against Aristotle’s metaphysics. Ironically he then used Aristotle’s scientific method to provide a foundation for the new science resulting in Descartes’s famous dualism. Thirdly, Spinoza, equally horrified by the amount of religious violence of his time, reacts against Descartes’s dualism, providing scholars with a monist metaphysics that would contribute greatly to the naturalisation of the Bible. This article will be relevant to theologians who wish to engage more fully with contemporary Western culture. (shrink)

Theologians are used to pointing the finger at European continental postmodernism when dealing with modern relativism. This article addresses a problem that is seldom highlighted within theology: modern relativism is the result of a series of epistemological discussions that took place during the early Enlightenment between scholars such as Rene Descartes, John Locke and Immanuel Kant. They were reacting, in part, to Aristotle’s metaphysics and logic. When the whole picture unravels, one immediately sees that modern relativism is deeply ingrained in (...) Western thought. In other words, modern relativism will not gather dust after the demise of postmodernism. To the contrary, this article would argue that modern relativism will continue to pose serious challenges to reformed churches in future. Pastors who want to engage with Western audiences will benefit from being made aware of this. Hopefully this will encourage theologians to re-evaluate the relevancy of reformed theological constructs in societies that are deeply steeped in relativist thought. (shrink)

Bijdragen aan een congres waarin de integriteit van juridische professionals bediscussieerd wordt.

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...) is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a (...) complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a (...) complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...) quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

Einstein's philosophy of physics was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy, on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the (...) doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

A Dutch 'folk theorem' holds that 'from exchange it comes to tears'. This seems to contradict the basic idea found in economics that exchange and trade can make both sides better off. We show that the 'folk theorem' has a better theoretical foundation than sometimes thought, as it is vindicated by the equilibrium of an exchange game with two-sided asymmetric information. We, then, explain the practical value of such 'folk wisdom' in the real world by showing why players might be (...) unlikely to learn such an equilibrium strategy. (shrink)

The major significance of the German naturalist-physician Johann Friedrich Blumenbach (1752–1840) as a topic of historical study is the fact that he was one of the first anthropologists to investigate humankind as part of natural history. Moreover, Blumenbach was, and continues to be, a central figure in debates about race and racism. How exactly did Blumenbach define race and races? What were his scientific criteria? And which cultural values did he bring to bear on his scheme? Little historical work has (...) been done on Blumenbach’s fundamental, influential race work. From his own time till today, several different pronouncements have been made by either followers or opponents, some accusing Blumenbach of being the fountainhead of scientific racism. By contrast, across early nineteenth-century Europe, not least in France, Blumenbach was lionized as an anti-racist whose work supported the unity of humankind and the abolition of slavery. This collection of essays considers how, with Blumenbach and those around him, the study of natural history and, by extension, that of science came to dominate the Western discourse of race. (shrink)

Information about the powers and abilities of acting entities is used to coordinate their actions in societies, either physical or digital. Yet, the commonsensical meaning of an acting entity being deemed able to do something is still missing from the existing specification languages for the web or for multi-agent systems. We advance a general purpose abstract logical account of evidence-based ability. A basic model can be thought of as the ongoing trace of a multi-agent system. Every state records systemic confirmations (...) and disconfirmations of whether an acting entity is able to bring about something. Qualitative inductive reasoning is then used in order to infer what acting entities are deemed able to bring about in the multi-agent system. A temporalised modal language is used to talk about deemed ability, actual agency, and confirmation and disconfirmation of deemed ability. What constitutes a confirmation and a disconfirmation is left to the modeller as in general it depends on the application at hand. So to illustrate the methodology we propose two extended examples, one in practical philosophy, the other in system engineering. We first use a logic of agency and ability to obtain a version of Mele’s general practical abilities. Then, we look at the management of abilities in a supervised system. (shrink)

We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will (...) be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein (1965) and Hartle (1968), intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program - notably the one due to Farhi, Goldstone, and Gutmann (1989) as completed by Van Wesep (2006) - in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. In combination with our interpretational context, this technical improvement circumvents valid criticisms that earlier derivations of the Born rule have provoked, especially to the effect that such derivations were mathematically flawed as well as circular. Furthermore, instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables. (shrink)

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that has been (...) proposed in previous work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL. (shrink)

We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment needed for their formalization, and (...) even simplify their logical formulation. (shrink)

We present the main logical theories of action. We distinguish theories identifying an action with its result from theories studying actions in terms of both their results and the means that result is obtained. The first family includes most prominently the logic of seeing-to-it-that and the logic of bringing-it-about-that. The second includes propositional dynamic logic and its variants. For all these logics we overview their extensions by other modalities such as modal operators of knowledge, belief, and obligation.

Optimism has reigned supreme for a long time regarding the potential of education (schooling) to address the many societal ailments that humankind has had to deal with. The outbreak of the COVID-19 pandemic in March 2020 shifted all such aspirations to the back-burner. Now, after just more than a year after the initial outbreak of the pandemic, the question can be raised whether those who managed the pandemic in the educational context followed the correct policies and instituted the correct (ethical, (...) moral) measures in combatting the pandemic. This comparison between the situation in the Netherlands and South Africa reveals that although the role-players in both countries had a good understanding of the situation and of their duties in such conditions, they tended to treat education as just another facet of society, thereby demonstrating a lack of empathy with the unique demands of education (schooling). CONTRIBUTION: In this article, the authors investigate the governance performance of two different countries during the first year of the COVID-19 pandemic concerning education and judge that performance based on a Biblically driven ethical-moral-pedagogical framework. (shrink)

Optimism has reigned supreme for a long time regarding the potential of education (schooling) to address the many societal ailments that humankind has had to deal with. The outbreak of the COVID-19 pandemic in March 2020 shifted all such aspirations to the back-burner. Now, after just more than a year after the initial outbreak of the pandemic, the question can be raised whether those who managed the pandemic in the educational context followed the correct policies and instituted the correct (ethical, (...) moral) measures in combatting the pandemic. This comparison between the situation in the Netherlands and South Africa reveals that although the role-players in both countries had a good understanding of the situation and of their duties in such conditions, they tended to treat education as just another facet of society, thereby demonstrating a lack of empathy with the unique demands of education (schooling). CONTRIBUTION: In this article, the authors investigate the governance performance of two different countries during the first year of the COVID-19 pandemic concerning education and judge that performance based on a Biblically driven ethical-moral-pedagogical framework. (shrink)

The South African-Dutch research group responsible for this article started its activities in 2012 by looking at religious tolerance as a means of addressing the tendency for religious intolerance, extremism and fundamentalism. While tolerance seemed to be a promising way to counter religious intolerable behaviour, some shortcomings also became apparent. For example, the concept of tolerance includes an aspect of passivity towards others who adhere to another religion. The concept also does not appear to be able to respond to attitudes (...) and values such as respect, human rights and diversity. Accurate investigation of this problem, both conceptually and empirically, led to the understanding that hospitality is a concept that embodies more active adaptation to those who are different. Hospitality, therefore, seems to be a more promising concept than tolerance for reducing religious tension between individuals and groups. The inner contradiction discovered by Derrida in the notion of hospitality does not detract from the concept of being defined from a Biblical point of view. Hospitality can also be taught to young people. Although there are no formal provisions for hospitality in the national curricula, an analysis of the Dutch and South African national curricula shows that there is room for hospitality education. (shrink)

The Dutch philosopher of religion Hent de Vries has explored and complicated the boundaries between religion and modern thought in order to create the space for an innovative “minimal theology.” This article reconstructs de Vries's interpretation of the changes in Theodor W. Adorno's thought between Dialectic of Enlightenment and Negative Dialectics in order to demonstrate its fecundity for a philosophical account of otherness. It also examines and defends de Vries's own rhetorical mode of reading texts as an exemplary approach to (...) philosophical dialogue. Finally, however, the essay challenges de Vries's privileging of the religious as the site of ethical relationality and his intentional bracketing of Adorno's critical social theory. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} of A, which is a commutative Rickart C*-algebra in the topos of functors from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}A}$$\end{document} to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns–Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} for A = B(H). (shrink)

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting (...) attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation. (shrink)

The Dutch philosopher of religion Hent de Vries has explored and complicated the boundaries between religion and modern thought in order to create the space for an innovative “minimal theology.” This article reconstructs de Vries's interpretation of the changes in Theodor W. Adorno's thought between Dialectic of Enlightenment and Negative Dialectics in order to demonstrate its fecundity for a philosophical account of otherness. It also examines and defends de Vries's own rhetorical mode of reading texts as an exemplary approach to (...) philosophical dialogue. Finally, however, the essay challenges de Vries's privileging of the religious as the site of ethical relationality and his intentional bracketing of Adorno's critical social theory. (shrink)

We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a logic of agency. (...) In particular, we apply it to reason about the resource-sensitive use of artefacts. (shrink)

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...) extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatisation and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the l.. (shrink)