Related papers: The Problem of Analogical Inference in Inductive L…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
Induction is a form of reasoning that starts with a particular example and generalizes to a rule, namely, a hypothesis. However, establishing the truth of a hypothesis is problematic due to the potential occurrence of conflicting events,…
Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We provided in \cite{BaldwinBrincusI} extensions of first order logic by modified inferential definitions of the classical $\omega$-rule in $1$ or $2$ sorts. These logics are categorical in the inferential sense. Arithmetic has a unique…
We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based…
We examine the relationship between the Bayesian and information-theoretic formulations of source separation algorithms. This work makes use of the relationship between the work of Claude E. Shannon and the "Recent Contributions" by Warren…
Anhomomorphic logic is a new interpretation of Quantum Theory (due to R. Sorkin). It is a histories formulation (c.f. consistent histories, quantum measure theory). In this approach, reality is a co-event, which is essentially an assignment…
We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
We propose an intersubjective epistemic approach to foundations of probability theory and statistical inference, based on relative entropy and category theory, and aimed to bypass the mathematical and conceptual problems of existing…
Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an…
This paper provides a proof that Tennant's logical system entails a paradox that is called Core logic paradox, in reference to the new name given by Tennant to his intuitionistic relevant logic.
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…