A semantical approach to equilibria and rationality

Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and with the environment. Rational behaviors are achieved not only through conscious reasoning, but also through spontaneous stabilization at equilibrium points. Formal theories of rationality are usually guided by informal intuitions, which are acquired by observing some concrete economic, biological, or network processes. Treating such processes as instances of computation, we reconstruct and refine some basic notions of equilibrium and rationality from the some basic structures of computation. It is, of course, well known that equilibria arise as fixed points; the point is that semantics of computation of fixed points seems to be providing novel methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

Axioms for Recursion in Call-by-Value

We propose an axiomatization of fixpoint operators in typed call-by-value programming languages, and give its justifications in two ways. First, it is shown to be sound and complete for the notion of uniform T-fixpoint operators of Simpson and Plotkin. Second, the axioms precisely account for Filinski's fixpoint operator derived from an iterator (infinite loop constructor) in the presence of firstclass continuations, provided that we define the uniformity principle on such an iterator via a notion of effect-freeness (centrality). We then explain how these two results are related in terms of the underlying categorical structures

Perceiving ‘capability’ within dynamic capabilities: the role of owner-manager self-efficacy

This article combines two popular, yet separate concepts, dynamic capabilities and self-efficacy. Both are concerned with ability / capability and offer potentially valuable synergies. As such, our in-depth qualitative study based in three micro-enterprises in the United Kingdom (UK), investigated, ‘what role(s) may owner-manager perceived self-efficacy play as a micro-foundation of dynamic capabilities in micro-enterprises?’ Our findings show that perceived self-efficacy can influence dynamic capability enactment in multifaceted ways and even suggest that in some cases, perceived self-efficacy is a crucial component of dynamic capabilities, without which there may be no such capability. These insights help open up the black box of dynamic capabilities by contributing important knowledge to the growing body of research into the micro-foundations of such capabilities. Furthermore, our study illuminates the importance of idiosyncratic micro-foundations of dynamic capabilities in micro-enterprises and expands extant knowledge of the potential effects of self-efficacy in the small business and entrepreneurship domain

Nominal Lawvere Theories

Abstract. Lawvere theories provide a category theoretic view of equa-tional logic, identifying equational theories with small categories equipped with finite products. This formulation allows equational theories to be investigated as first class mathematical entities. However, many formal systems, particularly in computer science, are described by equations modulated by side conditions asserting the “freshness of names”; these may be expressed as theories of Nominal Equational Logic (NEL). This paper develops a correspondence between NEL-theories and certain cat-egories that we call nominal Lawvere theories