Prime implicate generation in equational logic

The work presented in this memoir deals with the generation of prime implicates in ground equational logic, i.e., of the most general consequences of formulae containing equations and disequations between ground terms.It is divided in three parts. First, two calculi that generate implicates are defined. Their deductive-completeness is proved, meaning they can both generate all the implicates up to redundancy of equational formulae.Second, a tree data structure to store the generated implicates is proposed along with algorithms to detect redundancies and prune the branches of the tree accordingly. This data structure is adapted to the different kinds of clauses (with and without function symbols, with and without constraints) and to the various formal definitions of redundancy used in the calculi since each calculus uses different -- although similar -- redundancy criteria. Termination and correction proofs are provided with each algorithm. Finally, an experimental evaluation of the different prime implicate generation methods based on research prototypes written in Ocaml is conducted including a comparison with state-of-the-art prime implicate generation tools. This experimental study is used to identify the most efficient variants of the proposed algorithms. These show promising results overstepping the state of the art.Ce mémoire présente le résultat de mon travail de thèse sur la génération d'impliqués premiers en logique équationnelle fermée, i.e., la génération des conséquences les plus générales de formules logiques contenants des équations et des disequations entre termes sans variables. Ce mémoire est divisé en trois parties. Tout d'abord, deux calculs de génération d'impliqués sont définis. Leur complétude pour la déduction est prouvée, ce qui signifie qu'ils sont tous deux capables de générer l'ensemble des impliqués modulo redondance d'une formule équationnelle fermée. Dans une deuxième partie, une structure de données arborescente est proposée pour stocker les impliqués générés, accompagnée d'algorithmes pour déceler les redondances et couper les branches de l'arbre lorsque c'est nécessaire. Cette structure de données est adaptée aux différents types de clauses (avec et sans symboles de fonctions, avec et sans contraintes) ainsi qu'aux différentes notions de redondance utilisées dans les calculs. En effet, chaque calcul utilise un critère de redondance légèrement différent des autres. Les preuves de correction et de terminaison des algorithmes sont fournies pour chaque algorithme. Enfin, une évaluation expérimentale des différentes méthodes de génération d'impliqués premiers est réalisée. Pour cela, un prototype de ces méthodes, écrit en Ocaml est comparé à des outils de génération d'impliqués premiers récents.Les résultats de ces expériences sont utilisés pour identifier les variantes les plus efficaces des algorithmes proposés. Les résultats sont prometteurs et dans la plupart des cas, meilleurs que ceux de l'état de l'art

Prime implicate generation in equational logic

The work presented in this memoir deals with the generation of prime implicates in ground equational logic, i.e., of the most general consequences of formulae containing equations and disequations between ground terms.It is divided in three parts. First, two calculi that generate implicates are defined. Their deductive-completeness is proved, meaning they can both generate all the implicates up to redundancy of equational formulae.Second, a tree data structure to store the generated implicates is proposed along with algorithms to detect redundancies and prune the branches of the tree accordingly. This data structure is adapted to the different kinds of clauses (with and without function symbols, with and without constraints) and to the various formal definitions of redundancy used in the calculi since each calculus uses different -- although similar -- redundancy criteria. Termination and correction proofs are provided with each algorithm. Finally, an experimental evaluation of the different prime implicate generation methods based on research prototypes written in Ocaml is conducted including a comparison with state-of-the-art prime implicate generation tools. This experimental study is used to identify the most efficient variants of the proposed algorithms. These show promising results overstepping the state of the art.Ce mémoire présente le résultat de mon travail de thèse sur la génération d'impliqués premiers en logique équationnelle fermée, i.e., la génération des conséquences les plus générales de formules logiques contenants des équations et des disequations entre termes sans variables. Ce mémoire est divisé en trois parties. Tout d'abord, deux calculs de génération d'impliqués sont définis. Leur complétude pour la déduction est prouvée, ce qui signifie qu'ils sont tous deux capables de générer l'ensemble des impliqués modulo redondance d'une formule équationnelle fermée. Dans une deuxième partie, une structure de données arborescente est proposée pour stocker les impliqués générés, accompagnée d'algorithmes pour déceler les redondances et couper les branches de l'arbre lorsque c'est nécessaire. Cette structure de données est adaptée aux différents types de clauses (avec et sans symboles de fonctions, avec et sans contraintes) ainsi qu'aux différentes notions de redondance utilisées dans les calculs. En effet, chaque calcul utilise un critère de redondance légèrement différent des autres. Les preuves de correction et de terminaison des algorithmes sont fournies pour chaque algorithme. Enfin, une évaluation expérimentale des différentes méthodes de génération d'impliqués premiers est réalisée. Pour cela, un prototype de ces méthodes, écrit en Ocaml est comparé à des outils de génération d'impliqués premiers récents.Les résultats de ces expériences sont utilisés pour identifier les variantes les plus efficaces des algorithmes proposés. Les résultats sont prometteurs et dans la plupart des cas, meilleurs que ceux de l'état de l'art

Systematic Unfoldment of Differential Ontology from Qualitative Concept of Information

A certain philosophical ontology is presented as developed from a qualitative concept of information, leading to conclusive points of possible far-reaching relevance for philosophy and science

The Neural Representation of Concepts in Bilinguals: An Evaluation of Factors Influencing Cross-language Overlap Using fMRI-based Multivariate Pattern Analysis

161 p.The neurocognitive mechanisms that support the generalization of semantic representations across different languages remain to be determined. Current psycholinguistic models propose that semantic representations are likely to overlap across languages, although there is evidence also to the contrary. Neuroimaging studies observed that brain activity patterns associated with the meaning of words may be similar across languages. However, the factors that mediate cross-language generalization of semantic representations are not known. In a series of functional MRI research studies, we investigate how factors including state of visual awareness, depth of word processing and lexico-semantic characteristics of words influence cross-language generalization of semantic representations. Using multivariate pattern analysis, we found that fully conscious and deep processing of high concrete and high frequency words leads to above-chance cross-language generalization in putative areas of the semantic network. These results have ramifications for existing psycholinguistic models and theories of meaning representation.bcbl:basque center on cognition, brain & languag

Vagueness in mathematics talk

The Cockcroft Report claimed that "mathematics provides a means of communication which is powerful, concise and unambiguous". Such precision in language may be a conventional aim of mathematics, particularly when communicated in writing. Nonetheless, as this thesis demonstrates, vagueness is commonplace when people talk about mathematics. In this thesis, I examine the circumstances in which vagueness arises in mathematics talk, and consider the practical purposes which speakers achieve by means of vague utterances in this context. The empirical database, which is considered in Chapters 4 to 7, consists almost entirely of transcripts of mathematical conversations between adult interviewers (including myself) and one or two children. The data were collected from clinical interviews focused on a small number of tasks, and from fragments of teaching. For the most part, the pupils involved in the study were aged between 9 and 12, although the age-range in Chapter 7 extends from 4 to 25. I draw on a number of approaches to discourse associated with 'pragmatics' -a field of linguistics - to analyse the motives and communicative effectiveness of speakers who deploy vagueness in mathematics talk. I claim that, for these speakers, vagueness fulfills a number of purposes, especially 'shielding', i. e. self-protection against accusation of being wrong. Another purpose is to give approximate information; sometimes to achieve shielding, but also to provide the level of detail that is deemed to be appropriate in a given situation. A different purpose, associated with a particular form of vagueness (of reference), is to compensate for lexical gaps in pursuit of effective communication of concepts and ideas. I show, in particular, how speakers use the pronouns 'it' and 'you' in mathematics talk to communicate concepts and generalisations. Some consideration is given to the intentions of 'expert speakers of mathematics when they deploy vague language. Their purposes include some of those identified for novices. Teachers also use vagueness as a means of indirectness in addressing pupils; this strategy is associated with the redress of 'face threatening acts'. My thesis is that vagueness can be viewed and presented, not as a disabling feature of language, but as a subtle and versatile device which speakers can and do deploy to make mathematical assertions with as much precision, accuracy or as much confidence as they judge is warranted by both the content and the circumstances of their utterances. I report on the validation and generalisation of my findings by an Informal Research Group of school teachers, who transcribed and analysed their own classroom interactions using the methods I had developed

U+16E99

The general understanding and professional practice of graphic design have been shaped by the perspectives, needs, and desires of white, cis-gendered, heterosexual men in imperialist, capitalist societies. The tools, substrates, professional networks, institutions, processes, theories, grammars, and values that have come to define the discipline have been formed from this position. Consequently, graphic design primarily serves the needs of the settler in settler colonial regimes like the United States. This reality has prompted many designers like myself who come from colonized communities or whose identity troubles this rubric to question the framework of the discipline and our position within it. My thesis is rooted within this broader inquiry, which for me, as a Black and Indigenous person, began a few years ago through the emergence of two decolonial movements in the communities I call home: the BlackLivesMatter movement in Minneapolis following the live-streamed extra-judicial killing of Philando Castile by a White police officer; and the NoDAPL movement in Standing Rock which sought to prevent the construction of an oil pipeline across the river my tribe depends upon for water. The inquiries that evolved from the social and political contexts in which I began my formal design education have particular salience now amidst current manifestations of colonial oppression: a deadly global pandemic that has disproportionately claimed the lives of Black and Indigenous people due to the violence of structural inequities in the United States; the resurgence of the Keystone XL oil pipeline threatening the ecological sovereignty and well-being of numerous indigenous communities in the Midwest, including my own; and the nation wide uprisings sparked by the extra-judicial killing of George Floyd by Minneapolis police. As I write this, I can hear the whir of police and military helicopters surveilling the streets of Providence for protesters out past state-mandated curfew. My background and the urgent socio-political contexts surrounding my design education have forced me to seek out creative and subversive methodologies to bend a design discipline defined for the service of settler colonialism towards ongoing decolonial movements in Black and Indigenous communities. Using design in the service of decolonial movements will require new articulations of tools, substrates, networks, institutions, processes, theories, grammars, and values. Fortunately, there is a long tradition to draw from in marginalized communities of repurposing tools not designed for us to meet our own needs. Decolonization is not a destination along a binary array. Rather, it is a vector traversed through a lifelong practice seeking what lies beyond the decolonial horizon. In a decolonial design practice, design and the products of design are not an end; for endeavors with no end, process is the product. Design is the work that leads to and through the personal, interpersonal, and systemic work of decolonization. A radical design practice uses craft as a vehicle for the beyond, one of many possible methods that activate the decolonial moments, gestures, and utterances between people that triangulate new vectors for our collective liberation and help carry us there. As such, rather than catalog design works, the images in this publication utter a personal narrative of formative moments that transpired through the work of design. I am the work design helps make. U+16E99 is one articulation of a decolonial design practice uttered through the poetic grammars of Black, Indigenous, Queer, and Feminist thinkers, makers, and organizers. It is an attempt to define a trajectory for my own creative practice that centers my values, needs, and desires, while navigating the demands, precarities, and limitations of the academic institutions and settler colonial contexts in which this mapping takes place