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Rough set theory models uncertainty by approximating target concepts through lower and upper sets induced by indiscernibility, or more generally, by granulation relations in data tables. This perspective captures vagueness caused by limited…
Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical formulation of this problem, where operations on state-based…
Inconsistency in prediction problems occurs when instances that relate in a certain way on condition attributes, do not follow the same relation on the decision attribute. For example, in ordinal classification with monotonicity…
A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
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…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
Composing basic skills from simple tasks to accomplish composite tasks is crucial for modern intelligent systems. We investigate the in-context composition ability of language models to perform composite tasks that combine basic skills…
Realizing when a model is right for a wrong reason is not trivial and requires a significant effort by model developers. In some cases an input salience method, which highlights the most important parts of the input, may reveal problematic…
Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
We study in general algebras Gratzer's notion of congruence preserving function, characterizing functions in terms of stability under inverse image of particular Boolean algebras of subsets generated from any subset of the algebra.…
We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing…
Commonsense reasoning deals with the implicit knowledge that is well understood by humans and typically acquired via interactions with the world. In recent times, commonsense reasoning and understanding of various LLMs have been evaluated…
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall…
Systematic compositionality is the ability to recombine meaningful units with regular and predictable outcomes, and it's seen as key to humans' capacity for generalization in language. Recent work has studied systematic compositionality in…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is…
Large Language Models (LLMs) achieve strong performance in analyzing and generating text, yet they struggle with explicit, transparent, and verifiable reasoning over complex texts such as those containing debates. In particular, they lack…