An algebraic study of residuated ordered monoids and logics without exchange and contraction.

Thesis (Ph.D.)-University of Natal, Durban, 1998.Please refer to the thesis for the abstract

Towards a methodology for addressing missingness in datasets, with an application to demographic health datasets

Missing data is a common concern in health datasets, and its impact on good decision-making processes is well documented. Our study's contribution is a methodology for tackling missing data problems using a combination of synthetic dataset generation, missing data imputation and deep learning methods to resolve missing data challenges. Specifically, we conducted a series of experiments with these objectives; $a)$ generating a realistic synthetic dataset, $b)$ simulating data missingness, $c)$ recovering the missing data, and $d)$ analyzing imputation performance. Our methodology used a gaussian mixture model whose parameters were learned from a cleaned subset of a real demographic and health dataset to generate the synthetic data. We simulated various missingness degrees ranging from $10 \%$, $20 \%$, $30 \%$, and $40\%$ under the missing completely at random scheme MCAR. We used an integrated performance analysis framework involving clustering, classification and direct imputation analysis. Our results show that models trained on synthetic and imputed datasets could make predictions with an accuracy of $83 \%$ and $80 \%$ on $a)$ an unseen real dataset and $b)$ an unseen reserved synthetic test dataset, respectively. Moreover, the models that used the DAE method for imputed yielded the lowest log loss an indication of good performance, even though the accuracy measures were slightly lower. In conclusion, our work demonstrates that using our methodology, one can reverse engineer a solution to resolve missingness on an unseen dataset with missingness. Moreover, though we used a health dataset, our methodology can be utilized in other contexts.Comment: 16 pages and references, 5 figures and four tables, Paper accepted for presentation at SACAIR 2022 in Stellenbosch, Westen Cape, South Afric

Computing optimal strategies for a cooperative hat game

We consider a `hat problem' in which each player has a randomly placed stack of black and white hats on their heads, visible to the other player, but not the wearer. Each player must guess a hat position on their head with the goal of both players guessing a white hat. We address the question of finding the optimal strategy, i.e., the one with the highest probability of winning, for this game. We provide an overview of prior work on this question, and describe several strategies that give the best known lower bound on the probability of winning. Upper bounds are also considered here

Algebraizing deductive systems.

Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.Abstract available in PDF

Creating Diverse Play-Style-Centric Agents through Behavioural Cloning

Developing diverse and realistic agents in terms of behaviour and skill is crucial for game developers to enhance player satisfaction and immersion. Traditional game design approaches involve hand-crafted solutions, while learning game-playing agents often focuses on optimizing for a single objective, or play-style. These processes typically lack intuitiveness, fail to resemble realistic behaviour, and do not encompass a diverse spectrum of play-styles at varying levels of skill. To this end, our goal is to learn a set of policies that exhibit diverse behaviours or styles while also demonstrating diversity in skill level. In this paper, we propose a novel pipeline, called PCPG (Play-style-Centric Policy Generation), which combines unsupervised play-style identification and policy learning techniques to generate a diverse set of play-style-centric agents. The agents generated by the pipeline can effectively capture the richness and diversity of gameplay experiences in multiple video game domains, showcasing identifiable and diverse play-styles at varying levels of proficiency

On levine's notorious hat puzzle

The Levine hat game requires n players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. They are allowed a strategy session before the game, but no further communication. The players collectively win if and only if all their guesses are correct. In this paper we give an overview of what is known about strategies for this game, including an extended discussion of the case with n = 2 players (and a conjecture for an optimal strategy in this case). We also prove that Vn, the optimal value of the joint success probability in the n-player game, is a strictly decreasing function of n.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

On levine's notorious hat puzzle

The Levine hat game requires n players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. They are allowed a strategy session before the game, but no further communication. The players collectively win if and only if all their guesses are correct. In this paper, we give an overview of what is known about strategies for this game, including an extended discussion of the case with n =2 players (and a conjecture for an optimal strategy in this case). We also prove that Vn, the optimal value of the joint success probability in the n-player game, is a strictly decreasing function of n.SCOPUS: ch.binfo:eu-repo/semantics/publishe