Related papers: Principles and Examples of Plausible Reasoning and…

We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the…

Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can…

Logic reasoning has been critically needed in problem-solving and decision-making. Although Language Models (LMs) have demonstrated capabilities of handling multiple reasoning tasks (e.g., commonsense reasoning), their ability to reason…

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…

Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…

In spite of the rapidly increasing number of applications of machine learning in various domains, a principled and systematic approach to the incorporation of domain knowledge in the engineering process is still lacking and ad hoc solutions…

Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…

Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…

We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…

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…

This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an…

We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…

(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…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…

The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to…