Implementing probabilistic description logics: An application to image interpretation

This paper presents an application of an optimized implementation of a probabilistic description logic defined by Giugno and Lukasiewicz [9] to the domain of image interpretation. This approach extends a description logic with so-called probabilistic constraints to allow for automated reasoning over formal ontologies in combination with probabilistic knowledge. We analyze the performance of current algorithms and investigate new optimization techniques

Thinking through proliferations of geometries, fractions and parts : Conclusion and Summary of the work of Marilyn Strathern

Summary of Marilyn Strathern's contribution to anthropology and outline of the idea of geometrical anthropologyNon peer reviewe

How to Tell the Story? : On Story and Narrative in the Research Process – A pragmatic constructive approach

Note: the paper has been updated 24 August 2021. In this paper I investigate the problems of data collection, data analysis and the final communication of the results of our research, when doing social science that we, ourselves, are part of. Central to this are the concepts life world, language games and stories and narratives. How do we collect stories and narratives in the field, how do we construct scientific narratives that are both reliable and valid? And finally, how do we, as researchers present our newly constructed narrative to a – hopefully – interested audience? That is, how do you, as a consumer of scientific narratives, read what I have been writing? Finally, I will discuss the problem of handing over research results to the people that we are doing research with. This is all done within a framework of a pragmatic constructivist paradigm

Rethinking the role of the ‘fragile experts’ in the age of technique. Urban planners between specialization and ontological uncertainty

What are the attributes assumed by urban planning in the age of technique? How does it change and what is the role of planners today? To what extent is it possible to speak about the ‘fragility’ of planning’s epistemological bases, practices, design as well as cultural ambitions? Starting from these complex questions, the article suggests an exploration of the planners’ role(s) suspended between the limits of an increasingly specialized model of knowledge production and dissemination, on the one hand, and the need to combine this paradigm with the multiple challenges imposed by the complexity of contemporary urban scenarios, on the other. In the face of this tension, accentuated by the conditions of ontological uncertainty of today’s knowledge panorama, planners are called to recognize the fragility of (their) expert knowledge as well as the (inescapable) existence of forms of ‘asymmetrical relationality’. This would be the first step in the process of rethinking about the function and scope of planners in the face of the challenges posed by the immediate future – and among these, the contrast to scholarly isolation, as a tendency towards the isolation of knowledge from practices (and of ‘experts’ from society)

Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Boundary Algebra: A Simpler Approach to Boolean Algebra and the Sentential Connectives

Boundary algebra [BA] is a algebra of type , and a simplified notation for Spencer-Brown’s (1969) primary algebra. The syntax of the primary arithmetic [PA] consists of two atoms, () and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting, indifferently, the presence or absence of () into a PA formula yields a BA formula. The BA axioms are A1: ()()= (), and A2: “(()) [abbreviated ‘⊥’] may be written or erased at will,” implying (⊥)=(). The repeated application of A1 and A2 simplifies any PA formula to either () or ⊥. The basis for BA is B1: abc=bca (concatenation commutes & associates); B2, ⊥a=a (BA has a lower bound, ⊥); B3, (a)a=() (BA is a complemented lattice); and B4, (ba)a=(b)a (implies that BA is a distributive lattice). BA has two intended models: (1) the Boolean algebra 2 with base set B={(),⊥}, such that () ⇔ 1 [dually 0], (a) ⇔ a′, and ab ⇔ a∪b [a∩b]; and (2) sentential logic, such that () ⇔ true [false], (a) ⇔ ~a, and ab ⇔ a∨b [a∧b]. BA is a self-dual notation, facilitates a calculational style of proof, and simplifies clausal reasoning and Quine’s truth value analysis. BA resembles C.S. Peirce’s graphical logic, the symbolic logics of Leibniz and W.E. Johnson, the 2 notation of Byrne (1946), and the Boolean term schemata of Quine (1982).Boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; G. Spencer-Brown; C.S. Peirce; existential graphs

Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors

Boundary algebra [BA] is a simpler notation for Spencer-Brown’s (1969) primary algebra [pa], the Boolean algebra 2, and the truth functors. The primary arithmetic [PA] consists of the atoms ‘()’ and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting the presence or absence of () into a PA formula yields a BA formula. The BA axioms are "()()=()" (A1), and "(()) [=?] may be written or erased at will” (A2). Repeated application of these axioms to a PA formula yields a member of B= {(),?} called its simplification. (a) has two intended interpretations: (a) ? a? (Boolean algebra 2), and (a) ? ~a (sentential logic). BA is self-dual: () ? 1 [dually 0] so that B is the carrier for 2, ab ? a?b [a?b], and (a)b [(a(b))] ? a=b, so that ?=() [()=?] follows trivially and B is a poset. The BA basis abc= bca (Dilworth 1938), a(ab)= a(b), and a()=() (Bricken 2002) facilitates clausal reasoning and proof by calculation. BA also simplifies normal forms and Quine’s (1982) truth value analysis. () ? true [false] yields boundary logic.G. Spencer Brown; boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; C.S. Peirce; existential graphs.