Related papers: The Hamiltonian Syllogistic
This paper describes a formalism that subsumes Peterson's intermediate quantifier syllogistic system, and extends the ideas by van Eijck on Aristotle's logic. Syllogisms are expressed in a concise form making use of and extending the…
Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other…
This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are…
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are…
We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles…
I show how Hamilton's philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton's metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then…
The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…
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 first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
The Aristotelian syllogistic cannot account for the validity of many inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a)…
In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper 'On the interpretation of intuitionistic logic' "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
In 1834-1835, Hamilton published two papers that revolutionized classical mechanics. In these papers, he introduced the Hamilton-Jacobi equation, Hamilton's equations of motion and the principle of least action. These three formulations of…
150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical and…
We extend the language of the classical syllogisms with the sentence-forms "At most 1 p is a q" and "More than 1 p is a q". We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation…
Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also…
In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group…