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The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
State of the art machine learning algorithms are highly optimized to provide the optimal prediction possible, naturally resulting in complex models. While these models often outperform simpler more interpretable models by order of…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
With the rise of machine learning, there is a great deal of interest in treating programs as data to be fed to learning algorithms. However, programs do not start off in a form that is immediately amenable to most off-the-shelf learning…
Polar codes are the first error-correcting codes to provably achieve the channel capacity but with infinite codelengths. For finite codelengths the existing decoder architectures are limited in working frequency by the partial sums…
Human vision is able to compensate imperfections in sensory inputs from the real world by reasoning based on prior knowledge about the world. Machine learning has had a significant impact on computer vision due to its inherent ability in…
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…
Static program analysis by abstract interpretation is an efficient method to determine properties of embedded software. One example is value analysis, which determines the values stored in the processor registers. Its results are used as…
Symbolic learning represents the most straightforward approach to interpretable modeling, but its applications have been hampered by a single structural design choice: the adoption of propositional logic as the underlying language.…
The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory --…
Probabilistic programming languages (PPLs) are a popular tool for high-level modelling across many fields. They provide a range of algorithms for probabilistic inference, which analyse models by learning their parameters from a dataset or…
Using the programming language Haskell, we introduce an implementation of propositional calculus, number theory, and a simple imperative language that can evaluate arithmetic and boolean expressions. Finally, we provide an implementation of…
We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…
For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…