Related papers: An Algebraic Semantics for Possibilistic Logic
We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural…
Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…
Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras…
When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as…
In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can…
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
We study propositional and first-order G\"odel logics over infinitary languages which are motivated semantically by corresponding interpretations into the unit interval [0,1]. We provide infinitary Hilbert-style calculi for the particular…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
We present a proof-theoretic analysis of the logic NL$\lambda$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…