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To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…

A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…

Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…

Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

Concurrent to the rapid progress in the development of neural-network based models in areas like natural language processing and computer vision, the need for creating explanations for the predictions of these black-box models has risen…

Value-based static analysis techniques express computed program invariants as logical formula over program variables. Researchers and practitioners use these invariants to aid in software engineering and verification tasks. When selecting…

The alignment of autonomous agents with human values is a pivotal challenge when deploying these agents within physical environments, where safety is an important concern. However, defining the agent's objective as a reward and/or cost…

Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…

Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of…

In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract…

Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the…

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…

Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations…

Tabling for contextual abduction in logic programming has been introduced as a means to store previously obtained abductive solutions in one context to be reused in another context. This paper identifies a number of issues in the existing…