Related papers: Aristotle's Logic Computed by Parametric Probabili…
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…
Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
We present a coherence-based probability semantics and probability propagation rules for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
Abduction, first proposed in the setting of classical logics, has been studied with growing interest in the logic programming area during the last years. In this paper we study abduction with penalization in the logic programming framework.…
A major reason behind the success of probability calculus is that it possesses a number of valuable tools, which are based on the notion of probabilistic independence. In this paper, I identify a notion of logical independence that makes…
The Platonic Representation Hypothesis suggests that representations from neural networks are converging to a common statistical model of reality. We show that the existing metrics used to measure representational similarity are confounded…
Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…
Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
A population-based optimization algorithm was designed, inspired by two main thinking modes in philosophy, both based on dialectic concept and thesis-antithesis paradigm. They impose two different kinds of dialectics. Idealistic and…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…