Tilman Hinnerichs

Tilman Hinnerichs, Zhenwei Tang, Xi Peng et al. · utoronto

Ontologies are one of the richest sources of knowledge. Real-world ontologies often contain thousands of axioms and are often human-made. Hence, they may contain inconsistency and incomplete information which may impair classical reasoners to compute entailments that are considered as useful. To overcome these two challenges, we propose FALCON, a Fuzzy Ontology Neural reasoner to approximate reasoning over ALC ontologies. We provide an approximate technique for the model generation step in classical ALC reasoners. Our approximation is not guaranteed to construct exact logical models, but can approximate arbitrary models, which is notably faster for some large ontologies. Moreover, by sampling multiple approximate logical models, our technique supports approximate entailment also over inconsistent ontologies. Theoretical results show that more models generated lead to closer, i.e., faithful approximation of entailment over ALC entailments. Experimental results show that FALCON enables approximate reasoning and reasoning in the presence of inconsistency. Our experiments further demonstrate how ontologies can improve knowledge base completion in biomedicine by incorporating knowledge expressed in ALC.

Tilman Hinnerichs, Bart Swinkels, Jaap de Jong et al.

A core challenge in program synthesis is taming the large space of possible programs. Since program synthesis is essentially a combinatorial search, the community has sought to leverage powerful combinatorial constraint solvers. Here, constraints are used to express the program semantics, but not as a potentially potent tool to remove unwanted programs. Recent inductive logic programming approaches introduce constraints on the program's syntax to be synthesized. These syntactic constraints allow for checking and propagating a constraint without executing the program, and thus for arbitrary operators. In this work, we leverage syntactic constraints to model program spaces, defining not just solutions that are feasible, but also ones that are likely useful. To demonstrate this idea, we introduce BART, a solver that efficiently propagates and solves these constraints. We evaluate BART on program space enumeration tasks, finding that the constraints eliminate up to 99 percent of the program space, and that modeling program spaces significantly reduces enumeration time.

Tilman Hinnerichs, Robin Manhaeve, Giuseppe Marra et al.

Neuro-symbolic systems (NeSy), which claim to combine the best of both learning and reasoning capabilities of artificial intelligence, are missing a core property of reasoning systems: Declarativeness. The lack of declarativeness is caused by the functional nature of neural predicates inherited from neural networks. We propose and implement a general framework for fully declarative neural predicates, which hence extends to fully declarative NeSy frameworks. We first show that the declarative extension preserves the learning and reasoning capabilities while being able to answer arbitrary queries while only being trained on a single query type.

Tilman Hinnerichs, Reuben Gardos Reid, Jaap de Jong et al.

Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and many programmers' dream. Numerous synthesizers have been developed to tackle program synthesis, manifesting different ideas to approach the exponentially growing program space. While numerous smart program synthesis tools exist, reusing and remixing previously developed methods is tedious and time-consuming. We propose Herb.jl, a unifying program synthesis library written in the Julia programming language, to address these issues. Since current methods rely on similar building blocks, we aim to modularize the underlying synthesis algorithm into communicating and fully extendable sub-compartments, allowing for straightforward reapplication of these modules. To demonstrate the benefits of using Herb.jl, we show three common use cases: 1. how to implement a simple problem and grammar, and how to solve it, 2. how to implement a previously developed synthesizer with just a few lines of code, and 3. how to run a synthesizer against a benchmark.