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Given a trained neural network, can any specified output be generated by some input? Equivalently, does the network correspond to a function that is surjective? In generative models, surjectivity implies that any output, including harmful…
Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the…
Principles of cognitive economy would require that concepts about objects, properties and relations should be introduced only if they simplify the conceptualisation of a domain. Unexpectedly, classic logic conditionals, specifying…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…
Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that…
A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a…
Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…
Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence,…
We propose a society-first theory of normative appropriateness where individuals, modeled as pre-trained actors with cognitive architectures analogous to Large Language Models (LLMs), generate behavior via predictive pattern completion. Our…
Humans can generate reasonable answers to novel queries (Schulz, 2012): if I asked you what kind of food you want to eat for lunch, you would respond with a food, not a time. The thought that one would respond "After 4pm" to "What would you…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…