Related papers: Reasoning With Qualitative Probabilities Can Be Tr…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
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…
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
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…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
In order to give appropriate semantics to qualitative conditionals of the form "if A then normally B", ordinal conditional functions (OCFs) ranking the possible worlds according to their degree of plausibility can be used. An OCF accepting…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and…
The framework of Pearl's Causal Hierarchy (PCH) formalizes three types of reasoning: probabilistic (i.e. purely observational), interventional, and counterfactual, that reflect the progressive sophistication of human thought regarding…
As ontologies proliferate and automatic reasoners become more powerful, the problem of protecting sensitive information becomes more serious. In particular, as facts can be inferred from other facts, it becomes increasingly likely that…