Related papers: A minimalistic look at widening operators
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
We introduce extensions by rules of the extensional level of the Minimalist Foundation which turn out to be equivalent to constructive and classical axiomatic set theories.
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
Manual ontology construction takes time, resources, and domain specialists. Supporting a component of this process for automation or semi-automation would be good. This project and dissertation provide a Formal Concept Analysis and WordNet…
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
Lax extensions of set functors play a key role in various areas including topology, concurrent systems, and modal logic, while predicate liftings provide a generic semantics of modal operators. We take a fresh look at the connection between…
Natural Language Processing has moved rather quickly from modelling specific tasks to taking more general pre-trained models and fine-tuning them for specific tasks, to a point where we now have what appear to be inherently generalist…
Logical reasoning is essential for large language models (LLMs) to ensure accurate and coherent inference. However, LLMs struggle with reasoning order variations and fail to generalize across logically equivalent transformations. LLMs often…