Related papers: Non-termination Analysis of Logic Programs with In…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
This paper presents a new type analysis for logic programs. The analysis is performed with a priori type definitions; and type expressions are formed from a fixed alphabet of type constructors. Non-discriminative union is used to join type…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…
This paper proposes the use of Constraint Logic Programming (CLP) to model SQL queries in a data-independent abstract layer by focusing on some semantic properties for signalling possible errors in such queries. First, we define a…
The limit behavior of inductive logic programs has not been explored, but when considering incremental or online inductive learning algorithms which usually run ongoingly, such behavior of the programs should be taken into account. An…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…
Bounded verification has proved useful to detect bugs and to increase confidence in the correctness of a program. In contrast to unbounded verification, reasoning about calls via (bounded) inlining and about loops via (bounded) unrolling…
We present the notion of asymptotically non-terminating initial variable values for linear loop programs. Those values are directly associated to initial variable values for which the corresponding program does not terminate. Our…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument. A geometric nontermination argument is a finite representation of an infinite execution of the form $(\vec{x} +…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
Linear logic programming uses provability as the basis for computation. In the operational semantics based on provability, executing the additive-conjunctive goal $G_1 \& G_2$ from a program $P$ simply terminates with a success if both…
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs. To this end, a variety of acceleration techniques has been proposed. However, so far all of them have been monolithic, i.e., a…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic.…