Related papers: Conceptua: Institutions in a Topos
We introduce the concept of access-based intuitionistic knowledge which relies on the intuition that agent $i$ knows $\varphi$ if $i$ has found access to a proof of $\varphi$. Basic principles are distribution and factivity of knowledge as…
Due to the significant role that curiosity plays in our lives, several theoretical constructs, such as the information gap theory and compression progress theory, have sought to explain how we engage in its practice. According to the…
We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…
Integrated information theory (IIT) argues that the substrate of consciousness is a maximally irreducible complex of units. Together, subsets of the complex specify a cause-effect structure, composed of distinctions and their relations,…
Formal Concept Analysis (FCA) offers several tools for qualitative data analysis. One possibility is to group objects that share common attributes together and get a concept lattice that describes the data. Quite often the size of this…
This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and…
The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
This study provides a conceptual overview of the literature dealing with the process of citing documents (focusing on the literature from the recent decade). It presents theories, which have been proposed for explaining the citation…
In the framework of propositional {\L}ukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly…
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…
Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
Integer sequences are of central importance to the modeling of concepts admitting complete finitary descriptions. We introduce a novel view on the learning of such concepts and lay down a set of benchmarking tasks aimed at conceptual…
Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection…
In this paper we considered the extension of the First-order Logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term 'intension' derives from the traditional logical Frege-Russell's doctrine that an idea…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
This paper presents a study of how the theory of categories leads to the creation of non classical logical systems. In particular, the case of the elementary topos of graphs, where there are three other truth values different from false and…
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…