Related papers: Non-monotonic Extensions to Formal Concept Analysi…
Proof schemata are a variant of LK-proofs able to simulate various induction schemes in first-order logic by adding so called proof links to the standard first-order LK-calculus. Proof links allow proofs to reference proofs thus giving…
In knowledge discovery applications, the pattern set generated from data can be tremendously large and hard to explore by analysts. In the Formal Concept Analysis (FCA) framework, there have been studies to identify important formal…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
We seek to semantically describe a set of images, capturing both the attributes of single images and the variations within the set. Our procedure is analogous to Principle Component Analysis, in which the role of projection vectors is…
We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We…
Feature attribution methods, such as SHAP and LIME, explain machine learning model predictions by quantifying the influence of each input component. When applying feature attributions to explain language models, a basic question is defining…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
Concept-based interpretability methods offer a lens into the internals of foundation models by decomposing their embeddings into high-level concepts. These concept representations are most useful when they are compositional, meaning that…
Although computational complexity is a fundamental aspect of program behavior, it is often at odds with common type theoretic principles such as function extensionality, which identifies all functions with the same $\textit{input-output}$…
We develop a general framework (multidimensional asymptotic classes, or m.a.c.s) for handling classes of finite first order structures with a strong uniformity condition on cardinalities of definable sets: The condition asserts that…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
Concept Bottleneck Models (CBMs) are interpretable models that route predictions through a layer of human-interpretable concepts. While widely studied in vision and, more recently, in NLP, CBMs remain largely unexplored in multimodal…
In this paper we introduce a fuzzy constraint linear discriminant analysis (FC-LDA). The FC-LDA tries to minimize misclassification error based on modified perceptron criterion that benefits handling the uncertainty near the decision…
Correlated pattern mining has increasingly become an important task in data mining since these patterns allow conveying knowledge about meaningful and surprising relations among data. Frequent correlated patterns were thoroughly studied in…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Concept Bottleneck Models (CBMs) provide explicit interpretations for deep neural networks through concepts and allow intervention with concepts to adjust final predictions. Existing CBMs assume concepts are conditionally independent given…
Modeling an ontology is a hard and time-consuming task. Although methodologies are useful for ontologists to create good ontologies, they do not help with the task of evaluating the quality of the ontology to be reused. For these reasons,…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…