Related papers: Subjective probability, trivalent logics and compo…
Following {\L}ukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger-Horne-Zeilinger `paradox' is shown to be an artifact caused by unjustified use of…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability…
Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed sometimes, in both everyday discourse and academic research. This indicates that it is necessary to…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
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…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
Criticisms of so called `subjective probability' come on the one hand from those who maintain that probability in physics has only a frequentistic interpretation, and, on the other, from those who tend to `objectivise' Bayesian theory,…
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…
Penalty logic, introduced by Pinkas, associates to each formula of a knowledge base the price to pay if this formula is violated. Penalties may be used as a criterion for selecting preferred consistent subsets in an inconsistent knowledge…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
This paper investigates the contingency of logic within the framework of possible world semantics. Possible world semantics captures the meaning of necessitation, i.e., a statement is necessarily true if it holds in all possible worlds.…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
Principles of cognitive economy would require that concepts about objects, properties and relations should be introduced only if they simplify the conceptualisation of a domain. Unexpectedly, classic logic conditionals, specifying…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…