Search results for "Propositional calculus"
showing 4 items of 14 documents
Closed-Form Expressions for Global and Local Interpretation of Tsetlin Machines
2021
Tsetlin Machines (TMs) capture patterns using conjunctive clauses in propositional logic, thus facilitating interpretation. However, recent TM-based approaches mainly rely on inspecting the full range of clauses individually. Such inspection does not necessarily scale to complex prediction problems that require a large number of clauses. In this paper, we propose closed-form expressions for understanding why a TM model makes a specific prediction (local interpretability). Additionally, the expressions capture the most important features of the model overall (global interpretability). We further introduce expressions for measuring the importance of feature value ranges for continuous feature…
On Obtaining Classification Confidence, Ranked Predictions and AUC with Tsetlin Machines
2020
Tsetlin machines (TMs) are a promising approach to machine learning that uses Tsetlin Automata to produce patterns in propositional logic, leading to binary (hard) classifications. In many applications, however, one needs to know the confidence of classifications, e.g. to facilitate risk management. In this paper, we propose a novel scheme for measuring TM confidence based on the logistic function, calculated from the propositional logic patterns that match the input. We then use this scheme to trade off precision against recall, producing area under receiver operating characteristic curves (AUC) for TMs. Empirically, using four real-world datasets, we show that AUC is a more sensitive meas…
Quasivarieties of Algebras
2001
This chapter plays a twofold role in the book. Firstly, the chapter surveys basic facts about quasivarieties of algebras. These facts are widely utilised in the subsequent chapters devoted to algebraizable logics. Secondly, the chapter shows how the methods initially elaborated for protoalgebraic sentential logics in the first part can be also applied in the area of equational logic. Most of the results presented in this chapter are proved by way of adapting the purely consequential methods of sentential logic to the needs of the (quasi) equational systems associated with quasivarieties of algebras.
Awareness and partitional information structures
1994
This is the first of two papers where we present a formal model of unawareness. We contrast unawareness with certainty and uncertainty. A subject is certain of something when he knows that thing; he is uncertain when he does not know it, but he knows he does not: he is consciously uncertain. On the other hand, he is unaware of something when he does not know it, and he does not know he does not know, and so on ad infinitum: he does not perceive, does not have in mind, the object of knowledge. The opposite of unawareness is awareness, which includes certainty and uncertainty. This paper has three main purposes. First, we formalize the concept of awareness, and introduce a symmetry axiom whic…