Pierre Carbonnelle

Pierre Carbonnelle, Gottfried Schenner, Maurice Bruynooghe et al.

We analyze how symmetries can be used to compress structures (also known as interpretations) onto a smaller domain without loss of information. This analysis suggests the possibility to solve satisfiability problems in the compressed domain for better performance. Thus, we propose a 2-step novel method: (i) the sentence to be satisfied is automatically translated into an equisatisfiable sentence over a ``lifted'' vocabulary that allows domain compression; (ii) satisfiability of the lifted sentence is checked by growing the (initially unknown) compressed domain until a satisfying structure is found. The key issue is to ensure that this satisfying structure can always be expanded into an uncompressed structure that satisfies the original sentence to be satisfied. We present an adequate translation for sentences in typed first-order logic extended with aggregates. Our experimental evaluation shows large speedups for generative configuration problems. The method also has applications in the verification of software operating on complex data structures. Our results justify further research in automatic translation of sentences for symmetry reduction.

Pierre Carbonnelle, Joost Vennekens, Bart Bogaerts et al.

Many practical problems can be understood as the search for a state of affairs that extends a fixed partial state of affairs, the \emph{environment}, while satisfying certain conditions that are formally specified. Such problems are found in, e.g., engineering, law or economics. We study this class of problems in a context where some of the relevant information about the environment is not known by the user at the start of the search. During the search, the user may consider tentative solutions that make implicit hypotheses about these unknowns. To ensure that the solution is appropriate, these hypotheses must be verified by observing the environment. Furthermore, we assume that, in addition to knowledge of what constitutes a solution, knowledge of general laws of the environment is also present. We formally define partial solutions with enough verified facts to guarantee the existence of complete and appropriate solutions. Additionally, we propose an interactive system to assist the user in their search by determining 1) which hypotheses implicit in a tentative solution must be verified in the environment, and 2) which observations can bring useful information for the search. We present an efficient method to over-approximate the set of relevant information, and evaluate our implementation.

Pierre Carbonnelle, Matthias Van der Hallen, Marc Denecker

We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and meta-programming quantification. We also investigate the relationship with concepts in intensional logic. We present an extension of first-order logic to support such abstractions, and show that it allows writing expressions of knowledge that are elaboration tolerant. To avoid nonsensical sentences in this formalism, we refine the concept of well-formed sentences, and propose a method to verify well-formedness with a complexity that is linear with the number of tokens in the formula. We have extended FO(.), a Knowledge Representation language, and IDP-Z3, a reasoning engine for FO(.), accordingly. We show that this extension was essential in accurately modelling various problem domains in an elaboration-tolerant way, i.e., without reification.

Pierre Carbonnelle, Simon Vandevelde, Joost Vennekens et al.

Industry abounds with interactive configuration problems, i.e., constraint solving problems interactively solved by persons with the assistance of a computer. The computer program, called a configurator, needs to perform a variety of reasoning tasks with the (often incomplete) information that the user provides. Imperative programming approaches make such systems difficult to implement and maintain. Knowledge-based configurators have been proposed to help engineers solve such problems, but many challenges remain. We present IDP-Z3, a new reasoning engine for the FO(.) KR language, and we report on its use for building configurators automatically from a knowledge base.