Search results for "Propositional calculus"
showing 10 items of 14 documents
Mining Interpretable Rules for Sentiment and Semantic Relation Analysis Using Tsetlin Machines
2020
Tsetlin Machines (TMs) are an interpretable pattern recognition approach that captures patterns with high discriminative power from data. Patterns are represented as conjunctive clauses in propositional logic, produced using bandit-learning in the form of Tsetlin Automata. In this work, we propose a TM-based approach to two common Natural Language Processing (NLP) tasks, viz. Sentiment Analysis and Semantic Relation Categorization. By performing frequent itemset mining on the patterns produced, we show that they follow existing expert-verified rule-sets or lexicons. Further, our comparison with other widely used machine learning techniques indicates that the TM approach helps maintain inter…
Obligations and Conditionals
2015
The paper considers two kinds of medieval obligational disputations (positio, rei veritas) and the medieval genre of sophismata in relation to the kinds of inferences accepted in them. The main texts discussed are the anonymous Obligationes parisienses from the early 13th century and Richard Kilvington’s Sophismata from the early 14th century. Four different kinds of warranted transition from an antecedent to a consequent become apparent in the medieval discussions: (1) the strong logical validity of basic propositional logic, (2) analytic validity based on conceptual containment, (3) merely semantic impossibility of the antecedent being true without the consequent, and (4) intuitively true…
Regularly Algebraizable Logics
2001
A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a non-empty system E(p, q) of equivalence sentences such that E(p, q) ⊆ C(p, q).
Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability
2020
Despite significant effort, building models that are both interpretable and accurate is an unresolved challenge for many pattern recognition problems. In general, rule-based and linear models lack accuracy, while deep learning interpretability is based on rough approximations of the underlying inference. Using a linear combination of conjunctive clauses in propositional logic, Tsetlin Machines (TMs) have shown competitive performance on diverse benchmarks. However, to do so, many clauses are needed, which impacts interpretability. Here, we address the accuracy-interpretability challenge in machine learning by equipping the TM clauses with integer weights. The resulting Integer Weighted TM (…
On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators
2020
The Tsetlin Machine (TM) is a recent machine learning algorithm with several distinct properties, such as interpretability, simplicity, and hardware-friendliness. Although numerous empirical evaluations report on its performance, the mathematical analysis of its convergence is still open. In this article, we analyze the convergence of the TM with only one clause involved for classification. More specifically, we examine two basic logical operators, namely, the "IDENTITY"- and "NOT" operators. Our analysis reveals that the TM, with just one clause, can converge correctly to the intended logical operator, learning from training data over an infinite time horizon. Besides, it can capture arbit…
From Arithmetic to Logic based AI: A Comparative Analysis of Neural Networks and Tsetlin Machine
2020
Neural networks constitute a well-established design method for current and future generations of artificial intelligence. They depends on regressed arithmetic between perceptrons organized in multiple layers to derive a set of weights that can be used for classification or prediction. Over the past few decades, significant progress has been made in low-complexity designs enabled by powerful hardware/software ecosystems. Built on the foundations of finite-state automata and game theory, Tsetlin Machine is increasingly gaining momentum as an emerging artificial intelligence design method. It is fundamentally based on propositional logic based formulation using booleanized input features. Rec…
A Tsetlin Machine with Multigranular Clauses
2019
The recently introduced Tsetlin Machine (TM) has provided competitive pattern recognition accuracy in several benchmarks, however, requires a 3-dimensional hyperparameter search. In this paper, we introduce the Multigranular Tsetlin Machine (MTM). The MTM eliminates the specificity hyperparameter, used by the TM to control the granularity of the conjunctive clauses that it produces for recognizing patterns. Instead of using a fixed global specificity, we encode varying specificity as part of the clauses, rendering the clauses multigranular. This makes it easier to configure the TM because the dimensionality of the hyperparameter search space is reduced to only two dimensions. Indeed, it tur…
Measuring the Novelty of Natural Language Text Using the Conjunctive Clauses of a Tsetlin Machine Text Classifier
2020
Most supervised text classification approaches assume a closed world, counting on all classes being present in the data at training time. This assumption can lead to unpredictable behaviour during operation, whenever novel, previously unseen, classes appear. Although deep learning-based methods have recently been used for novelty detection, they are challenging to interpret due to their black-box nature. This paper addresses \emph{interpretable} open-world text classification, where the trained classifier must deal with novel classes during operation. To this end, we extend the recently introduced Tsetlin machine (TM) with a novelty scoring mechanism. The mechanism uses the conjunctive clau…
Logical Sentential Calculi Inspired by the Chrysippean Sentential Calculus
2021
The aim of the present paper is to consider an approach, different from that presented by J. Łukasiewicz, concerning the interpretation of the so-called stoic undemonstrables, which were given by Chrysippus. Stoic undemonstrables have been interpreted in two different ways: using the notion of “negation of a sentence” (Łukasiewicz) and using the notion of “a sentence inconsistent with a given one” (Mates). According to the Stoics, two sentences are inconsistent if one of them is negation of the other. The Mates’ interpretation generates five different inference rules. Based on one of these rules we can consider (with other undemonstrables) four different stoic propositional calculi. Taking …
The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems
2019
The recently introduced Tsetlin Machine (TM) has provided competitive pattern classification accuracy in several benchmarks, composing patterns with easy-to-interpret conjunctive clauses in propositional logic. In this paper, we go beyond pattern classification by introducing a new type of TMs, namely, the Regression Tsetlin Machine (RTM). In all brevity, we modify the inner inference mechanism of the TM so that input patterns are transformed into a single continuous output, rather than to distinct categories. We achieve this by: (1) using the conjunctive clauses of the TM to capture arbitrarily complex patterns; (2) mapping these patterns to a continuous output through a novel voting and n…