Related papers: From Propositional Logic to Plausible Reasoning: A…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
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 work contributes to the domains of Boolean algebra and of Bayesian probability, by proposing an algebraic extension of Boolean algebras, which implements an operator for the Bayesian conditional inference and is closed under this…
Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…
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…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
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…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there…
Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and…
In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation…