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AI systems are increasingly governed by natural language principles, yet a key challenge arising from reliance on language remains underexplored: interpretive ambiguity. As in legal systems, ambiguity arises both from how these principles…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
This paper introduces and outlines a new integrative field, Ideometrics. It is the systematic science of generating, evaluating, and prioritising ideas, based on the proposed sense of ideas and assigning value to information by the brain.…
In this paper we provide a formalism, Sudoku logic, in which a solution is logically deducible if for every cell of the grid we can provably exclude all but a single option. We prove that the deductive system of Sudoku logic is sound and…
Recent advancements in AI foundation models have made it possible for them to be utilized off-the-shelf for creative tasks, including ideating design concepts or generating visual prototypes. However, integrating these models into the…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
The puzzle method was introduced by Choi and Park as an effective method for finding non-singular characteristic maps over wedged simplicial complexes $K(J)$ obtained from a given simplicial complex $K$. We study further the mod 2 case of…
Su-Doku, a popular combinatorial puzzle, provides an excellent testbench for heuristic explorations. Several interesting questions arise from its deceptively simple set of rules. How many distinct Su-Doku grids are there? How to find a…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their…
Deep Neural Networks have achieved great success in some of the complex tasks that humans can do with ease. These include image recognition/classification, natural language processing, game playing etc. However, modern Neural Networks fail…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
Continuous adaptation allows survival in an ever-changing world. Adjustments in the synaptic coupling strength between neurons are essential for this capability, setting us apart from simpler, hard-wired organisms. How these changes can be…
This paper presents a comparative analysis of Sudoku-solving strategies, focusing on recursive backtracking and a heuristic-based constraint propagation method. Using a dataset of 500 puzzles across five difficulty levels (Beginner to…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…
The unification of statistical (data-driven) and symbolic (knowledge-driven) methods is widely recognised as one of the key challenges of modern AI. Recent years have seen large number of publications on such hybrid neuro-symbolic AI…
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically…
Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been…