Related papers: Fixpoint 3-valued semantics for autoepistemic logi…
We present a theoretical framework in which a document and an AI model engage in a transfinite fixed-point interaction that leads to stable semantic alignment. Building on the foundations of Alpay Algebra, we introduce a functorial system…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
We derive a Prolog theorem prover for an Intuitionistic Epistemic Logic by starting from the sequent calculus {\bf G4IP} that we extend with operator definitions providing an embedding in intuitionistic propositional logic ({\bf IPC}). With…
The supervaluationist approach to fixed-point semantics is, arguably, the most celebrated and studied competitor to the Strong Kleene approach within Kripkean truth. In this paper, we show how to obtain supervaluationist fixed-point…
Reasoning over streams of input data is an essential part of human intelligence. During the last decade {\em stream reasoning} has emerged as a research area within the AI-community with many potential applications. In fact, the increased…
Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a…
A fact apparently not observed earlier in the literature of nonmonotonic reasoning is that Reiter, in his default logic paper, did not directly formalize informal defaults. Instead, he translated a default into a certain natural language…
This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…
A wide variety of nonmonotonic semantics can be expressed as approximators defined under AFT (Approximation Fixpoint Theory). Using traditional AFT theory, it is not possible to define approximators that rely on information computed in…
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…
In most classical models of belief change, epistemic states are represented by theories (AGM) or formulas (Katsuno-Mendelzon) and the new pieces of information by formulas. The Representation Theorem for revision operators says that…
We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main…