Related papers: Hard Provability Logics
We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT.…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
We study the collection of first-order logical schemata all of whose instances are theorems of a given theory $T$; we call these the validities of $T$ ($\mathsf{V}(T)$). It is easy to see that if $T$ is a decidable theory, then…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
In this note we will introduce a class of search problems, called nested Polynomial Local Search (nPLS) problems, and show that definable NP search problems, i.e., $\Sigma^b_1$-definable functions in $T^2_2$ are characterized in terms of…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
In this paper we study the interaction between logic and probability. In particular, we show that the convex hull of evaluations of a broad class of logics is always effectively axiomatizable. We define a Birkhoff-style calculus for…
The purpose of the present paper is to analyze several variants of Solovay's theorem on the existence of doubly partially conservative sentences. First, we investigate $\Theta$ sentences that are doubly $(\Gamma, \Lambda)$-conservative over…
We robustify PCTL and PCTL*, the most important specification languages for probabilistic systems, and show that robustness does not increase the complexity of their model-checking problems.
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
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…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
Proof systems for the Relativized Propositional Calculus are defined and compared.
For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal…
A formula $\phi$ is called \emph{$n$-provable} in a formal arithmetical theory $S$ if $\phi$ is provable in $S$ together with all true arithmetical $\Pi_{n}$-sentences taken as additional axioms. While in general the set of all $n$-provable…
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…
We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of…