Related papers: Penalty logic and its Link with Dempster-Shafer Th…
The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…
Stemming from de Finetti's work on finitely additive coherent probabilities, the paradigm of coherence has been applied to many uncertainty calculi in order to remove structural restrictions on the domain of the assessment. Three possible…
We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson [14]. We develop a…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
Considerable attention has been given to the problem of non-monotonic reasoning in a belief function framework. Earlier work (M. Ginsberg) proposed solutions introducing meta-rules which recognized conditional independencies in a…
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…
Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
By analyzing the relationships among chance, weight of evidence and degree of beliefwe show that the assertion "probability functions are special cases of belief functions" and the assertion "Dempster's rule can be used to combine belief…
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…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
This paper presents a logic programming-based framework for policy-aware autonomous agents that can reason about potential penalties for non-compliance and act accordingly. While prior work has primarily focused on ensuring compliance, our…
Incidence Calculus and Dempster-Shafer Theory of Evidence are both theories to describe agents' degrees of belief in propositions, thus being appropriate to represent uncertainty in reasoning systems. This paper presents a straightforward…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…