Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al., allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original characterization of semantics for nested justification systems leads to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of their semantics and show that it is equivalent to the original one. Furthermore, we show how nested justification systems allow representing fixpoint definitions.

FOLD-RM is an automated inductive learning algorithm for learning default rules for mixed (numerical and categorical) data. It generates an (explainable) answer set programming (ASP) rule set for multi-category classification tasks while maintaining efficiency and scalability. The FOLD-RM algorithm is competitive in performance with the widely used, state-of-the-art algorithms such as XGBoost and multi-layer perceptrons, however, unlike these algorithms, the FOLD-RM algorithm produces an explainable model. FOLD-RM outperforms XGBoost on some datasets, particularly large ones. FOLD-RM also provides human-friendly explanations for predictions.

Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like machine-learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and $\mathrm{MV-Datalog}^\pm$ as extensions of Datalog and $\mathrm{Datalog}^\pm$ , respectively, to the fuzzy semantics of infinite-valued Łukasiewicz logic $\mathbf{L}$ as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model theoretic properties as Datalog. In particular, we show that (fuzzy) entailment can be decided via minimal fuzzy models. We show that when they exist, such minimal fuzzy models are unique and can be characterised in terms of a linear optimisation problem over the output of a fixed-point procedure. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending $\mathrm{Datalog}^\pm$ .

With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic abductive reasoning mechanisms, we synthesize conjunctions of literals that mimic rows of truth tables in classical or intermediate logics and we abduce conditional hypotheses that turn the theorems of classical or intermediate logics into theorems in intuitionistic logic. One step further, we generalize our abductive reasoning mechanism to synthesize more expressive sequent premises using a minimal set of canonical formulas, to which arbitrary formulas in the calculus can be reduced while preserving their provability. Organized as a self-contained literate Prolog program, the paper supports interactive exploration of its content and ensures full replicability of our results.

Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive, is not purely model-theoretic. As a result, certain properties of programs appear non-trivial to formalize in purely logical terms. For example, the current characterization of strong equivalence for LPODs, does not coincide with logical equivalence in some specific logic. This comes in sharp contrast with the well-known characterization of strong equivalence for classical logic programs, which coincides with logical equivalence in the logic of here-and-there. In this paper we obtain a purely logical characterization of strong equivalence for LPODs as logical equivalence in a four-valued logic. Moreover, we provide a new proof of the coNP-completeness of strong equivalence for LPODs, which has an interest in its own right since it relies on the special structure of such programs. Our results are based on the recent logical semantics of LPODs, a fact which we believe indicates that this new semantics may prove to be a useful tool in the further study of LPODs.

Building Information Modeling (BIM) produces three-dimensional object-oriented models of buildings combining the geometrical information with a wide range of properties about materials, products, safety, to name just a few. BIM is slowly but inevitably revolutionizing the architecture, engineering, and construction industry. Buildings need to be compliant with regulations about stability, safety, and environmental impact. Manual compliance checking is tedious and error-prone, and amending flaws discovered only at construction time causes huge additional costs and delays. Several tools can check BIM models for conformance with rules/guidelines. For example, Singapore’s CORENET e-Submission System checks fire safety. But since the current BIM exchange format only contains basic information about building objects, a separate, ad-hoc model pre-processing is required to determine, for example, evacuation routes. Moreover, they face difficulties in adapting existing built-in rules and/or adding new ones (to cater for building regulations, that can vary not only among countries but also among parts of the same city), if at all possible. We propose the use of logic-based executable formalisms (CLP and Constraint ASP) to couple BIM models with advanced knowledge representation and reasoning capabilities. Previous experience shows that such formalisms can be used to uniformly capture and reason with knowledge (including ambiguity) in a large variety of domains. Additionally, incorporating checking within design tools makes it possible to ensure that models are rule-compliant at every step. This also prevents erroneous designs from having to be (partially) redone, which is also costly and burdensome. To validate our proposal, we implemented a preliminary reasoner under CLP(Q/R) and ASP with constraints and evaluated it with several BIM models.

We present a neuro-symbolic visual question answering (VQA) pipeline for CLEVR, which is a well-known dataset that consists of pictures showing scenes with objects and questions related to them. Our pipeline covers (i) training neural networks for object classification and bounding-box prediction of the CLEVR scenes, (ii) statistical analysis on the distribution of prediction values of the neural networks to determine a threshold for high-confidence predictions, and (iii) a translation of CLEVR questions and network predictions that pass confidence thresholds into logic programmes so that we can compute the answers using an answer-set programming solver. By exploiting choice rules, we consider deterministic and non-deterministic scene encodings. Our experiments show that the non-deterministic scene encoding achieves good results even if the neural networks are trained rather poorly in comparison with the deterministic approach. This is important for building robust VQA systems if network predictions are less-than perfect. Furthermore, we show that restricting non-determinism to reasonable choices allows for more efficient implementations in comparison with related neuro-symbolic approaches without losing much accuracy.

Even though the core of the Prolog programming language has been standardized by ISO since 1995, it remains difficult to write complex Prolog programs that can run unmodified on multiple Prolog implementations. Indeed, implementations sometimes deviate from the ISO standard and the standard itself fails to cover many features that are essential in practice. Most Prolog applications thus have to rely on nonstandard features, often making them dependent on one particular Prolog implementation and incompatible with others. We examine one such Prolog application: ProB, which has been developed for over 20 years in SICStus Prolog. The article describes how we managed to refactor the codebase of ProB to also support SWI-Prolog, with the goal of verifying ProB’s results using two independent toolchains. This required a multitude of adjustments, ranging from extending the SICStus emulation in SWI-Prolog on to better modularizing the monolithic ProB codebase. We also describe notable compatibility issues and other differences that we encountered in the process, and how we were able to deal with them with few major code changes.