Deductive reasoning | EPFL Graph Search

Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning. Psychology is interested in deductive reasoning as a psychological process, i.e. how people actually draw inferences. Logic

Coevolutionary fuzzy modeling

Carlos Andres Peña Reyes

This thesis presents Fuzzy CoCo, a novel approach for system design, conducive to explaining human decisions. Based on fuzzy logic and coevolutionary computation, Fuzzy CoCo is a methodology for constructing systems able to accurately predict the outcome of a human decision-making process, while providing an understandable explanation of the underlying reasoning. Fuzzy logic provides a formal framework for constructing systems exhibiting both good numeric performance (precision) and linguistic representation (interpretability). From a numeric point of view, fuzzy systems exhibit nonlinear behavior and can handle imprecise and incomplete information. Linguistically, they represent knowledge in the form of rules, a natural way for explaining decision processes. Fuzzy modeling —meaning the construction of fuzzy systems— is an arduous task, demanding the identification of many parameters. This thesis analyses the fuzzy-modeling problem and different approaches to coping with it, focusing on evolutionary fuzzy modeling —the design of fuzzy inference systems using evolutionary algorithms— which constitutes the methodological base of my approach. In order to promote this analysis the parameters of a fuzzy system are classified into four categories: logic, structural, connective, and operational. The central contribution of this work is the use of an advanced evolutionary technique —cooperative coevolution— for dealing with the simultaneous design of connective and operational parameters. Cooperative coevolutionary fuzzy modeling succeeds in overcoming several limitations exhibited by other standard evolutionary approaches: stagnation, convergence to local optima, and computational costliness. Designing interpretable systems is a prime goal of my approach, which I study thoroughly herein. Based on a set of semantic and syntactic criteria, regarding the definition of linguistic concepts and their causal connections, I propose a number of strategies for producing more interpretable fuzzy systems. These strategies are implemented in Fuzzy CoCo, resulting in a modeling methodology providing high numeric precision, while incurring as little a loss of interpretability as possible. After testing Fuzzy CoCo on a benchmark problem —Fisher's Iris data— I successfully apply the algorithm to model the decision processes involved in two breast-cancer diagnostic problems: the WBCD problem and the Catalonia mammography interpretation problem. For the WBCD problem, Fuzzy CoCo produces systems both of high performance and high interpretability, comparable (if not better) than the best systems demonstrated to date. For the Catalonia problem, an evolved high-performance system was embedded within a web-based tool —called COBRA— for aiding radiologists in mammography interpretation. Several aspects of Fuzzy CoCo are thoroughly analyzed to provide a deeper understanding of the method. These analyses show the consistency of the results. They also help derive a stepwise guide to applying Fuzzy CoCo, and a set of qualitative relationships between some of its parameters that facilitate setting up the algorithm. Finally, this work proposes and explores preliminarily two extensions to the method: Island Fuzzy CoCo and Incremental Fuzzy CoCo, which together with the original CoCo constitute a family of coevolutionary fuzzy modeling techniques. The aim of these extensions is to guide the choice of an adequate number of rules for a given problem. While Island Fuzzy CoCo performs an extended search over different problem sizes, Incremental Fuzzy CoCo bases its search power on a mechanism of incremental evolution.

EPFL2002

CauseOccam: Learning Interpretable Abstract Representations in Reinforcement Learning Environments via Model Sparsity

Sergei Volodin

"I choose this restaurant because they have vegan sandwiches" could be a typical explanation we would expect from a human. However, current Reinforcement Learning (RL) techniques are not able to provide such explanations, when trained on raw pixels. RL algorithms for state-of-the-art benchmark environments are based on neural networks, which lack interpretability, because of the very factor that makes them so versatile – they have many parameters and intermediate representations. Enforcing safety guarantees is important when deploying RL agents in the real world, and guarantees require interpretability of the agent. Humans use short explanations that capture only the essential parts and often contain few causes to explain an effect. In our thesis, we address the problem of making RL agents understandable by humans. In addition to the safety concerns, the quest to mimic human-like reasoning is of general scientific interest, as it sheds light on the easy problem of consciousness. The problem of providing interpretable and simple causal explanations of agent's behavior is connected to the problem of learning good state representations. If we lack such a representation, any reasoning algorithm's outputs would be useless for interpretability, since even the "referents" of the "thoughts" of such a system would be obscure to us. One way to define simplicity of causal explanations via the sparsity of the Causal Model that describes the environment: the causal graph has the fewest edges connecting causes to their effects. For example, a model for choosing the restaurant that only depends on the cause "vegan" is simpler and more interpretable than a model that looks at each pixel of a photo of the menu of a restaurant, and possibly relies as well on spurious correlations, such the style of the menu. In this thesis, we propose a framework "CauseOccam" for model-based Reinforcement Learning where the model is regularized for simplicity in terms of sparsity of the causal graph it corresponds to. The framework contains a learned mapping from observations to latent features, and a model predicting latent features at the next time-steps given ones from the current time-step. The latent features are regularized with the sparsity of the model, compared to a more traditional regularization on the features themselves, or via a hand-crafted interpretability loss. To achieve sparsity, we use discrete Bernoulli variables with gradient estimation, and to find the best parameters, we use the primal-dual constrained formulation to achieve a target model quality. The novelty of this work is in learning jointly a sparse causal graph and the representation taking pixels as the input on RL environments. We test this framework on benchmark environments with non-trivial high-dimensional dynamics and show that it can uncover the causal graph with the fewest edges in the latent space. We describe the implications of our work for developing priors enforcing interpretability.

2021

Empirical validation of MesoHABSIM models developed with different habitat suitability criteria for bullhead cottus gobio L. as an indicator species

Mikolaj Stanislaw Adamczyk, Giovanni De Cesare, Piotr Parasiewicz

Application of instream habitat models such as the Mesohabitat Simulation Model (MesoHABSIM) is becoming increasingly popular. Such models can predict alteration to a river physical habitat caused by hydropower operation or river training. They are a tool for water management planning, especially in terms of requirements of the Water Framework Directive. Therefore, model verification studies, which investigate the accuracy and reliability of the results generated, are essential. An electrofishing survey was conducted in September 2014 on the Stura di Demonte River located in north-western Italy. One hundred and sixteen bullhead—Cottus gobio L.—were captured in 80 pre-exposed area electrofishing (PAE) grids. Observations of bullhead distribution in various habitats were used to validate MesoHABSIM model predictions created with inductive and deductive habitat suitability indices. The inductive statistical models used electrofishing data obtained from multiple mountainous streams, analyzed with logistic regression. The deductive approach was based on conditional habitat suitability criteria (CHSC) derived from expert knowledge and information gathered from the literature about species behaviour and habitat use. The results of model comparison and validation show that although the inductive models are more precise and reflect site- and species-specific characteristics, the CHSC model provides quite similar results. We propose to use inductive models for detailed planning of measures that could potentially impair riverine ecosystems at a local scale, since the CHSC model provides general information about habitat suitability and use of such models is advised in pre-development or generic scale studies. However, the CHSC model can be further calibrated with localized electrofishing data at a lower cost than development of an inductive model.

2019