Relating Justification Logic Modality and Type Theory in Curry–Howard Fashion

This dissertation is a work in the intersection of Justification Logic and Curry--Howard Isomorphism. Justification logic is an umbrella of modal logics of knowledge with explicit evidence. Justification logics have been used to tackle traditional problems in proof theory (in relation to Godel\u27s provability) and philosophy (Gettier examples, Russel\u27s barn paradox). The Curry--Howard Isomorphism or proofs-as-programs is an understanding of logic that places logical studies in conjunction with type theory and -- in current developments -- category theory. The point being that understanding a system as a logic, a typed calculus and, a language of a class of categories constitutes a useful discovery that can have many applications. The applications we will be mainly concerned with are type systems for useful programming language constructs. This work is structured in three parts: The first part is a a bird\u27s eye view into my research topics: intuitionistic logic, justified modality and type theory. The relevant systems are introduced syntactically together with main metatheoretic proof techniques which will be useful in the rest of the thesis. The second part features my main contributions. I will propose a modal type system that extends simple type theory (or, isomorphically, intuitionistic propositional logic) with elements of justification logic and will argue about its computational significance. More specifically, I will show that the obtained calculus characterizes certain computational phenomena related to linking (e.g. module mechanisms, foreign function interfaces) that abound in semantics of modern programming languages. I will present full metatheoretic results obtained for this logic/ calculus utilizing techniques from the first part and will provide proofs in the Appendix. The Appendix contains also information about an implementation of our calculus in the metaprogramming framework Makam. Finally, I conclude this work with a small ``outro\u27\u27, where I informally show that the ideas underlying my contributions can be extended in interesting ways

Pattern matching in compilers

In this thesis we develop tools for effective and flexible pattern matching. We introduce a new pattern matching system called amethyst. Amethyst is not only a generator of parsers of programming languages, but can also serve as an alternative to tools for matching regular expressions. Our framework also produces dynamic parsers. Its intended use is in the context of IDE (accurate syntax highlighting and error detection on the fly). Amethyst offers pattern matching of general data structures. This makes it a useful tool for implementing compiler optimizations such as constant folding, instruction scheduling, and dataflow analysis in general. The parsers produced are essentially top-down parsers. Linear time complexity is obtained by introducing the novel notion of structured grammars and regularized regular expressions. Amethyst uses techniques known from compiler optimizations to produce effective parsers.Comment: master thesi

Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output

Nominal Abstraction

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompassing these two features do not currently allow for the definition of relations that embody dynamic aspects related to binding, a capability needed in many reasoning tasks. We propose a new relation between terms called nominal abstraction as a means for overcoming this deficiency. We incorporate nominal abstraction into a rich logic also including definitions, generic quantification, induction, and co-induction that we then prove to be consistent. We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.Comment: To appear in the Journal of Information and Computatio

Animism rather than Shamanism: new approaches to what shamans do (for other animists)

What shamans do is sometimes said to involve possession by spirits. However, shamanism has also been defined in opposition to spirit possession. This chapter proposes that approaching shamans and their activities, ideas and communities via the perspective provided by recent re-examination and re-definition of "animism" may improve and and enrich scholarly understanding and analysis of the activities and unvolvements of shamans

Strong Normalization by Type-Directed Partial Evaluation and Run-Time Code Generation (Preliminary Version)

We investigate the synergy between type-directed partial evaluation and run-time code generation for the Caml dialect of ML. Type-directed partial evaluation maps simply typed, closed Caml values to a representation of their long beta-eta-normal form. Caml uses a virtual machine and has the capability to load byte code at run time. Representing the long beta-eta-normal forms as byte code gives us the ability to strongly normalize higher-order values (i.e., weak head normal forms in ML), to compile the resulting strong normal forms into byte code, and to load this byte code all in one go, at run time.We conclude this note with a preview of our current work on scalingup strong normalization by run-time code generation to the Camlmodule language

The Eco-Techno Spectrum: Exploring Knowledge Systems\u27 Challenges in Green Infrastructure Management

Infrastructure crises are not only technical problems for engineers to solve—they also present social, ecological, financial, and political challenges. Addressing infrastructure problems thus requires a robust planning process that includes examination of the social and ecological systems supporting infrastructure, alongside technical systems. An integrative Social, Ecological, and Technological Systems (SETS) analysis of infrastructure solutions can complement the planning process by revealing potential trade-offs that are often overlooked in standard procedures. We explore the interconnected SETS of the infrastructure problem in the US through comparative case studies of green infrastructure (GI) development in Portland and Baltimore. Currently a popular infrastructure solution to a wide variety of urban ills, GI is the use and mimicry of ecological components (e.g., plants) to perform municipal services (e.g., stormwater management). We develop the ecological-technological spectrum—or ‘eco-techno spectrum’—as a framing tool to bridge all three SETS dimensions. The eco-techno spectrum becomes a platform to explore the institutional knowledge system dynamics of GI development where social dimensions are organized across ecological and technological aspects of GI, exposing how governance differs across specific forms of ecological and technological hybridity. In this study, we highlight the knowledge system challenges of urban planning institutions as a key consideration in the realization of innovative infrastructure crisis ‘fixes.’ Disconnected definition and measurement of GI emerge as two distinct challenges across the knowledge systems examined. By revealing and discussing these challenges, we can begin to recognize—and better plan for—gaps in municipal planning knowledge systems, promoting decisions that address the roots of infrastructure crises rather than treating only their symptoms

lim+, delta+, and Non-Permutability of beta-Steps

Using a human-oriented formal example proof of the (lim+) theorem, i.e. that the sum of limits is the limit of the sum, which is of value for reference on its own, we exhibit a non-permutability of beta-steps and delta+-steps (according to Smullyan's classification), which is not visible with non-liberalized delta-rules and not serious with further liberalized delta-rules, such as the delta++-rule. Besides a careful presentation of the search for a proof of (lim+) with several pedagogical intentions, the main subject is to explain why the order of beta-steps plays such a practically important role in some calculi.Comment: ii + 36 page

Factoid question answering for spoken documents

In this dissertation, we present a factoid question answering system, specifically tailored for Question Answering (QA) on spoken documents. This work explores, for the first time, which techniques can be robustly adapted from the usual QA on written documents to the more difficult spoken documents scenario. More specifically, we study new information retrieval (IR) techniques designed for speech, and utilize several levels of linguistic information for the speech-based QA task. These include named-entity detection with phonetic information, syntactic parsing applied to speech transcripts, and the use of coreference resolution. Our approach is largely based on supervised machine learning techniques, with special focus on the answer extraction step, and makes little use of handcrafted knowledge. Consequently, it should be easily adaptable to other domains and languages. In the work resulting of this Thesis, we have impulsed and coordinated the creation of an evaluation framework for the task of QA on spoken documents. The framework, named QAst, provides multi-lingual corpora, evaluation questions, and answers key. These corpora have been used in the QAst evaluation that was held in the CLEF workshop for the years 2007, 2008 and 2009, thus helping the developing of state-of-the-art techniques for this particular topic. The presentend QA system and all its modules are extensively evaluated on the European Parliament Plenary Sessions English corpus composed of manual transcripts and automatic transcripts obtained by three different Automatic Speech Recognition (ASR) systems that exhibit significantly different word error rates. This data belongs to the CLEF 2009 track for QA on speech transcripts. The main results confirm that syntactic information is very useful for learning to rank question candidates, improving results on both manual and automatic transcripts unless the ASR quality is very low. Overall, the performance of our system is comparable or better than the state-of-the-art on this corpus, confirming the validity of our approach.En aquesta Tesi, presentem un sistema de Question Answering (QA) factual, especialment ajustat per treballar amb documents orals. En el desenvolupament explorem, per primera vegada, quines tècniques de les habitualment emprades en QA per documents escrit són suficientment robustes per funcionar en l'escenari més difícil de documents orals. Amb més especificitat, estudiem nous mètodes de Information Retrieval (IR) dissenyats per tractar amb la veu, i utilitzem diversos nivells d'informació linqüística. Entre aquests s'inclouen, a saber: detecció de Named Entities utilitzant informació fonètica, "parsing" sintàctic aplicat a transcripcions de veu, i també l'ús d'un sub-sistema de detecció i resolució de la correferència. La nostra aproximació al problema es recolza en gran part en tècniques supervisades de Machine Learning, estant aquestes enfocades especialment cap a la part d'extracció de la resposta, i fa servir la menor quantitat possible de coneixement creat per humans. En conseqüència, tot el procés de QA pot ser adaptat a altres dominis o altres llengües amb relativa facilitat. Un dels resultats addicionals de la feina darrere d'aquesta Tesis ha estat que hem impulsat i coordinat la creació d'un marc d'avaluació de la taska de QA en documents orals. Aquest marc de treball, anomenat QAst (Question Answering on Speech Transcripts), proporciona un corpus de documents orals multi-lingüe, uns conjunts de preguntes d'avaluació, i les respostes correctes d'aquestes. Aquestes dades han estat utilitzades en les evaluacionis QAst que han tingut lloc en el si de les conferències CLEF en els anys 2007, 2008 i 2009; d'aquesta manera s'ha promogut i ajudat a la creació d'un estat-de-l'art de tècniques adreçades a aquest problema en particular. El sistema de QA que presentem i tots els seus particulars sumbòduls, han estat avaluats extensivament utilitzant el corpus EPPS (transcripcions de les Sessions Plenaries del Parlament Europeu) en anglès, que cónté transcripcions manuals de tots els discursos i també transcripcions automàtiques obtingudes mitjançant tres reconeixedors automàtics de la parla (ASR) diferents. Els reconeixedors tenen característiques i resultats diferents que permetes una avaluació quantitativa i qualitativa de la tasca. Aquestes dades pertanyen a l'avaluació QAst del 2009. Els resultats principals de la nostra feina confirmen que la informació sintàctica és mol útil per aprendre automàticament a valorar la plausibilitat de les respostes candidates, millorant els resultats previs tan en transcripcions manuals com transcripcions automàtiques, descomptat que la qualitat de l'ASR sigui molt baixa. En general, el rendiment del nostre sistema és comparable o millor que els altres sistemes pertanyents a l'estat-del'art, confirmant així la validesa de la nostra aproximació