Related papers: Intuitionistic Epistemic Logic
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
The classical methods used by recursion theory and formal logic to block paradoxes do not work in quantum information theory. Since quantum information can exist as a coherent superposition of the classical ``yes'' and ``no'' states,…
In this paper we prove soundness and completeness of some epistemic extensions of G\"odel fuzzy logic, based on Kripke models in which both propositions at each state and accessibility relations take values in [0,1]. We adopt belief as our…
The classical belief revision framework, as proposed by Alchourron, Gardenfors, and Makinson, involves the revision of a theory based on eight postulates. In this paper, we focus on the exploration of a revision theory grounded in quantum…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
Representing knowledge as high-dimensional vectors in a continuous semantic vector space can help overcome the brittleness and incompleteness of traditional knowledge bases. We present a method for performing deductive reasoning directly in…
The crisis in the reproducibility of experiments invites a re-evaluation of methods of inquiry and validation procedures. The text challenges current assumptions of knowledge acquisition and introduces G-complexity for defining decidable…
Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this…
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
The definition of negation has to be referred to the totality of a theory and at last to what is defined as the organization of a scientific theory; in other words, the definition of negation is of a structural kind, rather than of an…
The rapid evolution of artificial intelligence has led to expectations of transformative impact on science, yet current systems remain fundamentally limited in enabling genuine scientific discovery. This perspective contends that progress…
In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of…
A classical logic exhibits a threefold inner structure comprising an algebra of propositions `A', a space of ``truth values'' `V', and a distinguished family of mappings `phi' from propositions to truth values. Classically A is a Boolean…
We present three different functional interpretations of intuitionistic linear logic ILL and show how these correspond to well-known functional interpretations of intuitionistic logic IL via embeddings of IL into ILL. The main difference…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
There has been a longstanding dispute over which formalism is the best for representing knowledge in AI. The well-known "declarative vs. procedural controversy" is concerned with the choice of utilizing declarations or procedures as the…
Despite extensive research efforts in recent years, computational argumentation (CA) remains one of the most challenging areas of natural language processing. The reason for this is the inherent complexity of the cognitive processes behind…
For a computational system to be intelligent, it should be able to perform, at least, basic deductions. Nonetheless, since deductions are, in some sense, equivalent to tautologies, it seems that they do not provide new information. The…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…