Layer by layer - Combining Monads

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e. layers of the language, which then provides a monad structure to the composition of layers, or (ii) identifies precisely the algebraic obstacles to the existence of a distributive law and gives a best approximant language. The running example will involve three layers: a basic imperative language enriched first by adding non-determinism and then probabilistic choice. The first extension works seamlessly, but the second encounters an obstacle, which results in a best approximant language structurally very similar to the probabilistic network specification language ProbNetKAT

Condition/Decision Duality and the Internal Logic of Extensive Restriction Categories

In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to form new conditions, though they only play a supporting role in aiding branching statements choose a branch to follow. On the other hand, in the graphical representation they are typically presented as decisions, intrinsically capable of directing control flow yet mostly oblivious to Boolean combination. While categorical treatments of flowchart languages are abundant, none of them provide a treatment of this dual nature of predicates. In the present paper, we argue that extensive restriction categories are precisely categories that capture such a condition/decision duality, by means of morphisms which, coincidentally, are also called decisions. Further, we show that having these categorical decisions amounts to having an internal logic: Analogous to how subobjects of an object in a topos form a Heyting algebra, we show that decisions on an object in an extensive restriction category form a De Morgan quasilattice, the algebraic structure associated with the (three-valued) weak Kleene logic $\mathbf{K}^w_3$. Full classical propositional logic can be recovered by restricting to total decisions, yielding extensive categories in the usual sense, and confirming (from a different direction) a result from effectus theory that predicates on objects in extensive categories form Boolean algebras. As an application, since (categorical) decisions are partial isomorphisms, this approach provides naturally reversible models of classical propositional logic and weak Kleene logic.Comment: 19 pages, including 6 page appendix of proofs. Accepted for MFPS XXX

Rhetoric and Reality in the Tax Law of Charity

This Article contrasts the rhetoric of public benefit connected to charity in the law with the reality of private control of charitable organizations. It argues that the tension between the rhetoric and reality have produced norms of entitlement that undermine taxation. It offers an approach to the role of charity under the law by defining the obligations of government in a just society, qualifying the economic framework dominant in the literature concerning charities, and identifying what private charity can achieve that governments cannot. This Article concludes by endorsing the charitable deduction in the tax law on terms consistent with this revised approach

Diversity, Disadvantage and Differential Outcomes: An analysis of Samoan students narratives of schooling

Social justice discourses, particularly those attentive to the politics of difference, suggest that the perspectives of least-advantaged groups need to be taken into account when endeavouring to realise social justice in education for these groups. In this paper, we analyse narratives on schooling produced by one cohort of least-advantaged students, namely Samoan students attending state-designated disadvantaged secondary schools in Queensland, Australia. Specifically, the narratives of educational disadvantage provided by Samoan students are analysed. The focus is on 'the what' (the knowledge to be transmitted) and 'the how' (the teacher-student relations) of pedagogy in state-designated disadvantaged schools. Attention is paid to the contradictory and ambivalent discourses inherent in these narratives, particularly in terms of realising socially just pedagogic practices

Categories of Timed Stochastic Relations

AbstractStochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior. These languages essentially denote continuous-time stochastic processes, obtained through an operational semantics in a probabilistic transition system. In this paper we seek a more descriptive foundation for the semantics of stochastic behavior using categories and monads. We model a first-order imperative language with stochastic delay by identifying probabilistic choice and delay as separate effects, modeling each with a monad, and combining the monads to build a model for the stochastic language

Does power unify a society?

After an introductory consideration on the specificity of philosophy and social philosophy about the socio-historical world, which can no longer be summarized under the name of “politics”, the essay advances a concept of society not as a unity of individuals, territorially or culturally secluded, but as a network of linguistic games, institutions and differentiated spheres. The result is a concept of power constitutively in the plural, which is thought as primarily organizing and collective. The main question, which is only extrinsically negotiable in terms of justice, results in the problem of how to avoid that a sphere predominates over the remaining ones, thus compressing the contributions, potentialities and inclusive capacity of each one.Tras considerar la especificidad de la filosofía y de la filosofía social con respecto al mundo histórico-social, que ya no se puede definir bajo el término “política”, el artículo propone un concepto de sociedad no como conjunto de individuos desde un punto de vista territorial o cultural, sino como red de juegos, instituciones o ámbitos diferenciados. De ahí procede un concepto de poder constitutivamente al plural, considerado antes que todo como organizante y colectivo. El eje principal –que solo extrínsecamente se puede solucionar en términos de justicia– atañe al problema de cómo evitar que un ámbito subyugue a los demás, llegando a reprimir las contribuciones, las potencialidades y capacidades inclusivas de cada uno de ellos

The Good Samaritan and the Hygienic Cook: A Cautionary Tale About Linguistic Data

When developing formal theories of the meaning of language, it is appropriate to consider how apparent paradoxes and conundrums of language are best resolved. But if we base our analysis on a small sample of data then we may fail to take into account the influence of other aspects of meaning on our intuitions. Here we consider the so-called Good Samaritan Paradox (Prior, 1958), where we wish to avoid any implication that there is an obligation to rob someone from "You must help a robbed man". We argue that before settling on a formal analysis of such sentences, we should consider examples of the same form, but with intuitively ?different entailments ? such as "You must use a clean knife" ? and also actively seek other examples that exhibit similar contrasts in meaning, even if they do not exemplify the phenomena that is under investigation. This can refine our intuitions and help us to attribute aspects of interpretation to the various facets of meaning