Related papers: The Problem of Analogical Inference in Inductive L…
Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…
Starting from the Boolean notion of logical proportion in Piaget's sense, which turns out to be equivalent to analogical proportion, this note proposes a definition of analogical proportion between numerical values based on triangular norms…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
We develop a Gentzen-style proof theory for super-Belnap logics (extensions of the four-valued Dunn-Belnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
There are several major proposals for treating donkey anaphora such as discourse representation theory and the likes, or E-Type theories and the likes. Every one of them works well for a set of specific examples that they use to demonstrate…
While analogies are a common way to evaluate word embeddings in NLP, it is also of interest to investigate whether or not analogical reasoning is a task in itself that can be learned. In this paper, we test several ways to learn basic…
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
We investigate the relation of countable closed subsets of the reals with respect to continuous monotone embeddability; we show that there are exactly aleph_1 many equivalence classes with respect to this embeddability relation. This is an…
In this article, we survey some controversial problems concerning the idea of erasing Which Way information proposed in recent years. A statistical examination of these proposals suggests that whenever the Bayesian rule is taken into…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
Although Large Language Models (LLMs) have demonstrated impressive formal reasoning abilities, they often break down when problems require complex proof planning. One promising approach for improving LLM reasoning abilities involves…
We consider models for inference which involve observers which may have multiple copies, such as in the Sleeping Beauty problem. We establish a framework for describing these problems on a probability space satisfying Kolmogorov's axioms,…
This paper proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the…
In his book `Physics and Philosophy', Heisenberg suggested that the quantum world is one of ``potentialities or possibilities'' and that the classical realm is one of ``things or facts''. After ascertaining that his categories most…
We introduce the intuitive method to select an analytic Abel function of an analytic function f at a non-fixpoint. Due to the complexity of this method by involving matrix inversion of increasing size there is little known about its…
Primal logic arose in access control; it has a remarkably efficient (linear time) decision procedure for its entailment problem. But primal logic is a general logic of information. In the realm of arbitrary items of information (infons),…
We propose an information-theoretic alternative to the popular Cronbach alpha coefficient of reliability. Particularly suitable for contexts in which instruments are scored on a strictly nonnumeric scale, our proposed index is based on…