Wikidata constraints, albeit useful, are represented and processed in an incomplete, ad hoc fashion. Constraint declarations do not fully express their meaning, and thus do not provide a precise, unambiguous basis for constraint specification, or a logical foundation for constraint-checking implementations. In prior work we have proposed a logical framework for Wikidata as a whole, based on multi-attributed relational structures (MARS) and related logical languages. In this paper we explain how constraints are handled in the proposed framework, and show that nearly all of Wikidata's existing property constraints can be completely characterized in it, in a natural and economical fashion. We also give characterizations for several proposed property constraints, and show that a variety of non-property constraints can be handled in the same framework.

Answer Set Programming (ASP) has become a popular and quite sophisticated approach to declarative problem solving. This is arguably due to its attractive modeling-grounding-solving workflow that provides an easy approach to problem solving, even for laypersons outside computer science. Unlike this, the high degree of sophistication of the underlying technology makes it increasingly hard for ASP experts to put ideas into practice. For addressing this issue, this tutorial aims at enabling users to build their own ASP-based systems. More precisely, we show how the ASP system CLINGO can be used for extending ASP and for implementing customized special-purpose systems. To this end, we propose two alternatives. We begin with a traditional AI technique and show how meta programming can be used for extending ASP. This is a rather light approach that relies on CLINGO's reification feature to use ASP itself for expressing new functionalities. Unlike this, the major part of this tutorial uses traditional programming (in PYTHON) for manipulating CLINGO via its application programming interface. This approach allows for changing and controlling the entire model-ground-solve workflow of ASP. Central to this is CLINGO's new Application class that allows us to draw on CLINGO's infrastructure by customizing processes similar to the one in CLINGO. For instance, we may engage manipulations to programs' abstract syntax trees, control various forms of multi-shot solving, and set up theory propagators for foreign inferences. Another cross-sectional structure, spanning meta as well as application programming, is CLINGO's intermediate format, ASPIF, that specifies the interface among the underlying grounder and solver. We illustrate the aforementioned concepts and techniques throughout this tutorial by means of examples and several non-trivial case-studies.

The focus of the 2018 Logic and Practice of Programming workshop was on logic and declarative languages for the practice of programming. Of particular interest were languages (1) that have a clear semantic foundation, so that they can be used for concise modeling of complex application problems, facilitating formal proofs and automated analysis, and (2) that are also implementable, so that the implementations can run as specified, as part of real applications. Also of interest were (a) the design of declarative languages, libraries, and tools that facilitate the construction of complex systems and applications, (b) approaches to integrate declarative and procedural programming, and (c) the use of declarative languages to facilitate other programming paradigms, e.g., distributed programming. The target audience for these languages was students who wish to model complex application problems, and practitioners who want to use them. The goal of the workshop was to bring together the best people and best languages, tools, and ideas to help improve logic languages for the practice of programming and to improve the practice of programming with logic and declarative programming.

Multi-attributed relational structures (MARSs) have been proposed as a formal data model for generalized property graphs, along with multi-attributed rule-based predicate logic (MARPL) as a useful rule-based logic in which to write inference rules over property graphs. Wikidata can be modelled in an extended MARS that adds the (imprecise) datatypes of Wikidata. The rules of inference for the Wikidata ontology can be modelled as a MARPL ontology, with extensions to handle the Wikidata datatypes and functions over these datatypes. Because many Wikidata qualifiers should participate in most inference rules in Wikidata a method of implicitly handling qualifier values on a per-qualifier basis is needed to make this modelling useful. The meaning of Wikidata is then the extended MARS that is the closure of running these rules on the Wikidata data model. Wikidata constraints can be modelled as multi-attributed predicate logic (MAPL) formulae, again extended with datatypes, that are evaluated over this extended MARS.

A core task in process mining is process discovery which aims to learn an accurate process model from event log data. In this paper, we propose to use (block-) structured programs directly as target process models so as to establish connections to the field of program synthesis and facilitate the translation from abstract process models to executable processes, e.g., for robotic process automation. Furthermore, we develop a novel bottom-up agglomerative approach to the discovery of such structured program process models. In comparison with the popular top-down recursive inductive miner, our proposed agglomerative miner enjoys the similar theoretical guarantee to produce sound process models (without deadlocks and other anomalies) while exhibiting some advantages like avoiding silent activities and accommodating duplicate activities. The proposed algorithm works by iteratively applying a few graph rewriting rules to the directly-follows-graph of activities. For real-world (sparse) directly-follows-graphs, the algorithm has quadratic computational complexity with respect to the number of distinct activities. To our knowledge, this is the first process discovery algorithm that is made for the purpose of program synthesis. Experiments on the BPI-Challenge 2020 dataset and the Karel programming dataset have demonstrated that our proposed algorithm can outperform the inductive miner not only according to the traditional process discovery metrics but also in terms of the effectiveness in finding out the true underlying structured program from a small number of its execution traces.

We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical statements, such as type inference, suggesting missing assumptions and completing equalities. To train language models for formal mathematics, we propose a novel skip-tree task. We find that models trained on the skip-tree task show surprisingly strong mathematical reasoning abilities, and outperform models trained on standard skip-sequence tasks. We also analyze the models' ability to formulate new conjectures by measuring how often the predictions are provable and useful in other proofs.

This paper continues the line of research aimed at investigating the relationship between logic programs and first-order theories. We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion in this context, and describe preliminary experiments with the use of two software tools, anthem and vampire, for verifying the correctness of programs with input and output. Proofs of theorems are based on a lemma that relates the semantics of programs studied in this paper to stable models of first-order formulas. This paper is under consideration for acceptance in Theory and Practice of Logic Programming.

Action selection policies (ASPs), used to compose low-level robot skills into complex high-level tasks are commonly represented as neural networks (NNs) in the state of the art. Such a paradigm, while very effective, suffers from a few key problems: 1) NNs are opaque to the user and hence not amenable to verification, 2) they require significant amounts of training data, and 3) they are hard to repair when the domain changes. We present two key insights about ASPs for robotics. First, ASPs need to reason about physically meaningful quantities derived from the state of the world, and second, there exists a layered structure for composing these policies. Leveraging these insights, we introduce layered dimension-informed program synthesis (LDIPS) - by reasoning about the physical dimensions of state variables, and dimensional constraints on operators, LDIPS directly synthesizes ASPs in a human-interpretable domain-specific language that is amenable to program repair. We present empirical results to demonstrate that LDIPS 1) can synthesize effective ASPs for robot soccer and autonomous driving domains, 2) requires two orders of magnitude fewer training examples than a comparable NN representation, and 3) can repair the synthesized ASPs with only a small number of corrections when transferring from simulation to real robots.

Recent trends in AI verification and Explainable AI have raised the question of whether AI planning techniques can be verified. In this paper, we present a novel resource logic, the Proof Carrying Plans (PCP) logic that can be used to verify plans produced by AI planners. The PCP logic takes inspiration from existing resource logics (such as Linear logic and Separation logic) as well as Hoare logic when it comes to modelling states and resource-aware plan execution. It also capitalises on the Curry-Howard approach to logics, in its treatment of plans as functions and plan pre- and post-conditions as types. This paper presents two main results. From the theoretical perspective, we show that the PCP logic is sound relative to the standard possible world semantics used in AI planning. From the practical perspective, we present a complete Agda formalisation of the PCP logic and of its soundness proof. Moreover, we showcase the Curry-Howard, or functional, value of this implementation by supplementing it with the library that parses AI plans into Agda's proofs automatically. We provide evaluation of this library and the resulting Agda functions.

Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP(A C)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP(A C) can be exploited for effective problem solving in a rich framework. This work is under consideration for acceptance in Theory and Practice of Logic Programming.