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We propose a set of compositional design patterns to describe a large variety of systems that combine statistical techniques from machine learning with symbolic techniques from knowledge representation. As in other areas of computer science…
For Latin squares the units (rows and columns) have fixed sum. The same holds for rows, columns, and blocks in Sudokus. Summing the elements of a unit yields a linear equation, and the set of all such equations forms a system of linear…
Thinking is one of the most interesting mental processes. Its complexity is sometimes simplified and its different manifestations are classified into normal and abnormal, like the delusional and disorganized thought or the creative one. The…
The rules of Sudoku are often specified using twenty seven \texttt{all\_different} constraints, referred to as the {\em big} \mrules. Using graphical proofs and exploratory logic programming, the following main and new result is obtained:…
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology. We present their construction from square-tiled shapes, discuss some of the underlying mathematics and describe how they are naturally associated…
Memristor networks are capable of low-power and massive parallel processing and information storage. Moreover, they have presented the ability to apply for a vast number of intelligent data analysis applications targeting mobile edge…
Pulli Kolam is an ancient mathematical artform that is still practiced today in south India by over a quarter million people. "Pulli" in the Tamil language means dots. A specific type of pulli kolam is "sikku" kolam where a series of dots…
We introduce modeLing, a novel benchmark of Linguistics Olympiad-style puzzles which tests few-shot reasoning in AI systems. Solving these puzzles necessitates inferring aspects of a language's grammatical structure from a small number of…
In this paper, we discuss different models for human logic systems and describe a game with nature. G\"odel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…
Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control…
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to…
Our goal is to $\textit{efficiently}$ discover a compact set of temporal logic rules to explain irregular events of interest. We introduce a neural-symbolic rule induction framework within the temporal point process model. The negative…
Reliable perception of the environment is a key enabler for autonomous systems, where calibration and localization tasks often rely on robust visual markers. We introduce the PuzzlePole, a new type of fiducial markers derived from the…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
Existing reasoning datasets saturate and fail to test abstract, multi-step problems, especially pathfinding and complex rule constraint satisfaction. We introduce SPaRC (Spatial Pathfinding Reasoning Challenge), a dataset of 1,000 2D grid…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
Exploring the capabilities of Large Language Models (LLMs) in puzzle solving unveils critical insights into their potential and challenges in AI, marking a significant step towards understanding their applicability in complex reasoning…