Related papers: Knowledge Theoretic Properties of Topological Spac…
We introduce the logic $\sf ITL^e$, an intuitionistic temporal logic based on structures $(W,\preccurlyeq,S)$, where $\preccurlyeq$ is used to interpret intuitionistic implication and $S$ is a $\preccurlyeq$-monotone function used to…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…
We propose a society-first theory of normative appropriateness where individuals, modeled as pre-trained actors with cognitive architectures analogous to Large Language Models (LLMs), generate behavior via predictive pattern completion. Our…
We propose a formal foundation for cognition rooted in algebraic topology, built on a Homological Parity Principle. This posits that even-dimensional homology represents stable Structure/Context (e.g., generative models), while…
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative…
Human explanations of natural language, rationales, form a tool to assess whether models learn a label for the right reasons or rely on dataset-specific shortcuts. Sufficiency is a common metric for estimating the informativeness of…
Research on knowledge graph embeddings has recently evolved into knowledge base embeddings, where the goal is not only to map facts into vector spaces but also constrain the models so that they take into account the relevant conceptual…
With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging…
The ability to interpret the mental state of another agent based on its behavior, also called Theory of Mind (ToM), is crucial for humans in any kind of social interaction. Artificial systems, such as intelligent assistants, would also…
We study notions of (virtual) group knowledge and group belief within multi-agent evidence models, obtained by extending the topological semantics of evidence-based belief and fallible knowledge from individuals to groups. We completely…
We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it…
We consider propositional modal logic with two modal operators $\Box$ and $\D$. In topological semantics $\Box$ is interpreted as an interior operator and $\D$ as difference. We show that some important topological properties are…
We show that a collection of three-sorted set-theoretic formulae, denoted TLQSR and which admits a restricted form of quantification over individual and set variables, has a solvable satisfiability problem by proving that it enjoys a small…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Reader curiosity, the drive to seek information, is crucial for textual engagement, yet remains relatively underexplored in NLP. Building on Loewenstein's Information Gap Theory, we introduce a framework that models reader curiosity by…
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…