Standardizing Nature : Tress, Woods, Lumber: Susana Reisman

"Dimensional lumber is largely used by the construction industry worldwide. In North America, a majority of households are built with a wooden structure or frame made from dimensional lumber. This series is about encouraging people to question and understand the reasoning (thought process) and decision-making behind the 'shape' of things. Moreover, it is about the natural resources we harness from the earth and the form, function and role they play in our everyday lives. Economies and industries are built around these decisions and they 'echo' off the center as rings in the core of a tree. Those standards set the 'tone' for future generations." -- Publisher's website

Discursive design thinking: the role of explicit knowledge in creative architectural design reasoning

The main hypothesis investigated in this paper is based upon the suggestion that the discursive reasoning in architecture supported by an explicit knowledge of spatial configurations can enhance both design productivity and the intelligibility of design solutions. The study consists of an examination of an architect’s performance while solving intuitively a well-defined problem followed by an analysis of the spatial structure of their design solutions. One group of architects will attempt to solve the design problem logically, rationalizing their design decisions by implementing their explicit knowledge of spatial configurations. The other group will use an implicit form of such knowledge arising from their architectural education to reason about their design acts. An integrated model of protocol analysis combining linkography and macroscopic coding is used to analyze the design processes. The resulting design outcomes will be evaluated quantitatively in terms of their spatial configurations. The analysis appears to show that an explicit knowledge of the rules of spatial configurations, as possessed by the first group of architects can partially enhance their function-driven judgment producing permeable and well-structured spaces. These findings are particularly significant as they imply that an explicit rather than an implicit knowledge of the fundamental rules that make a layout possible can lead to a considerable improvement in both the design process and product. This suggests that by externalizing th

Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties $R \leadsto Q$ on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no fairness and interleaving semantics, where $R$ and $Q$ are global state predicates. First, we show that verifying $R \leadsto Q$ for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy $R \leadsto Q$ is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates $R$ and $Q$, and automatically generates a parameterized protocol that satisfies $R \leadsto Q$ for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct $R$ predicates to different $Q$ predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols

Formalization of the fundamental group in untyped set theory using auto2

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

A Modal Logic for Subject-Oriented Spatial Reasoning

We present a modal logic for representing and reasoning about space seen from the subject\u27s perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete

Parameterized Model Checking of Token-Passing Systems

We revisit the parameterized model checking problem for token-passing systems and specifications in indexed $\textsf{CTL}^\ast \backslash \textsf{X}$. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ in uni-directional token rings can be reduced to checking rings up to some \emph{cutoff} size. Clarke et al. (2004) have shown a similar result for general topologies and indexed $\textsf{LTL} \backslash \textsf{X}$, provided processes cannot choose the directions for sending or receiving the token. We unify and substantially extend these results by systematically exploring fragments of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.Comment: We had to remove an appendix until the proofs and notations there is cleare