Related papers: Conjugate Logic
The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A…
We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
We consider the following model of decision-making by cognitive systems. We present an algorithm -- quantum-like representation algorithm (QLRA) -- which provides a possibility to represent probabilistic data of any origin by complex…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
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…
In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which features of quantum mechanics can be…
Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They…
We compare different epistemic notions in the presence of awareness of propositional variables: the logics of implicit knowledge (in which explicit knowledge is definable), explicit knowledge, and speculative knowledge. Different notions of…
In this paper, we generalize epistemic logic so that it can help reason about ways of combining common knowledge and distributed knowledge such as "common distributed knowledge", "distributed common knowledge", "distributed common…
In this paper we present the fundamentals of the so-called algebraic approach to propositional quantum logics. We define the set of formulas describing quantum reality as a free algebra freely generated by the set of quantum propositional…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Quantum information processing rests on our ability to manipulate quantum superpositions through coherent unitary transformations. In reality the quantum information processor (a linear ion trap, or cavity qed implementation for example)…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We use a novel type of epistemic logic, employing comparative knowledge assertions, to analyze the relative epistemic powers of individuals or groups of agents. Such comparative assertions can express that a group has the potential to…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…