In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum (...) logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages. (shrink)

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, (...) can be translated into classical logic by introducing additional intensional operators into the language. Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic. (shrink)

We investigate indeterminism in physical observations. For this, we introduce a distinction between genuinely indeterministic observational processes, and fully deterministic observational processes, which we analyze by drawing a parallel between the localization properties of microscopic entities, like electrons, and the lateralization properties of macroscopic entities, like simple elastic bands. We show that by removing the randomness incorporated in certain of our observational processes, acquiring over them a better control, we also alter these processes in such a radical way that in (...) the end they do not correspond anymore to the observation of the same property. We thus conclude that a certain amount of indeterminism must be accepted and welcomed in our physical observations, as we cannot get rid of it without also diminishing our discriminative power. We also provide in our analysis some elements of clarification regarding the non-spatial nature of microscopic entities, which we illustrate by using an analogy with the process of objectification of human concepts. Finally, the important notion of relational properties is properly defined, and the role played by indeterminism in their characterization clarified. (shrink)

At the 1927 Como conference Bohr spoke the famous words “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” However, if the Copenhagen interpretation really adheres to this motto, why then is there this nagging feeling of conflict when comparing it with realist interpretations? Surely what one can say about nature should in a certain sense be interpretation independent. In this paper I take Bohr’s (...) motto seriously and develop a quantum logic that avoids assuming any form of realism as much as possible. To illustrate the non-triviality of this motto, a similar result is first derived for classical mechanics. It turns out that the logic for classical mechanics is a special case of the quantum logic thus derived. Some hints are provided as to how these logics are to be used in practical situations and finally, I discuss how some realist interpretations relate to these logics. (shrink)

This article addresses and resolves some issues of relational, Kripke-style, semantics for the logics of bounded lattice expansions with operators of well-defined distribution types, focusing on the case where the underlying lattice is not assumed to be distributive. It therefore falls within the scope of the theory of Generalized Galois Logics, introduced by Dunn, and it contributes to its extension. We introduce order-dual relational semantics and present a semantic analysis and completeness theorems for non-distributive lattice logic with n -ary additive (...) or multiplicative operators, with negation operators modally interpreted as impossibility and unnecessity, as well as with implication connectives. Order-dual relational semantics shares with the generalized Kripke frames, or the bi-approximation semantics approach, the use of both a satisfaction and a co-satisfaction relation, but it also responds to the recently voiced concerns of Craig, Haviar and Conradie about the relative non-intuitiveness of the 2-sorted semantics of the aforementioned approaches. In this article, we provide a standard interpretation of modalities and natural interpretations of both negation and implication, despite the absence of distribution. Thereby, our results contribute in creating the necessary background for research in non-distributive logics with modalities variously interpreted as dynamic, temporal etc, by analogy to the classical case. (shrink)

In an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalising the well-known Gödel–McKinsey–Tarski translation of intuitionistic logic into S4. Došen's translation worked well for (variants of) BCI and stronger systems (BCW, BCK), but not for systems below BCI. Dropping structural rules results in logic systems without distribution. In this article, we show, via translation, that every substructural (indeed, every non-distributive) logic is a fragment of a corresponding sorted, residuated (multi) (...) modal logic. At the conceptual and philosophical level, the translation provides a classical interpretation of the meaning of the logical operators of various non-distributive propositional calculi. Technically, it allows for an effortless transfer of results, such as compactness and the Löwenheim-Skolem property and it opens up new directions for deducing properties of substructural logic systems by establishing appropriate transfer theorems. (shrink)

In their target article, Wang and Busemeyer (2013) discuss question order effects in terms of incompatible projectors on a Hilbert space. In a similar vein, Blutner recently presented an orthoalgebraic query language essentially relying on dynamic update semantics. Here, I shall comment on some interesting analogies between the different variants of dynamic semantics and generalized quantum theory to illustrate other kinds of order effects in human cognition, such as belief revision, the resolution of anaphors, and default reasoning that result from (...) the crucial non-commutativity of mental operations upon the belief state of a cognitive agent. (shrink)

The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have two contradictory pictures of reality but also compelled to abandon the objectiveness of the truth values, “true” and “false”. Yet, even if we could accept wave-like behavior of quantum particles as the best explanation for the build-up of an interference pattern in (...) the double-slit experiment, without the objectivity of the truth values we would never have certainty regarding any statement about the world. The present paper discusses ways to reconcile the correct description of the double-slit experiment with the objectiveness of “true” and “false”. (shrink)

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...) parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras. They are combined into a uniform system via a mechanism preventing the simultaneous realization of perspectives. Gleason’s theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic macro-systems using the framework of symbolic dynamics. Finally, we discuss several ideas that are useful for justifying complementarity in cognitive systems. (shrink)

In this paper we show how ideas coming from two areas of research in logic can reinforce each other. The first such line of inquiry concerns the "dynamic turn" in logic and especially the formalisms inspired by Propositional Dynamic Logic (PDL); while the second line concerns research into the logical foundations of Quantum Physics, and in particular the area known as Operational Quantum Logic, as developed by Jauch and Piron (Helve Phys Acta 42: 842-848, 1969), Pirón (Foundations of Quantum Physics, (...) 1976). By bringing these areas together we explain the basic ingredients of Dynamic Quantum Logic, a new direction of research in the logical foundations of physics. (shrink)

The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions between subsystems of a global physical system. Similarly, epistemic (...) logic is the logic of socially-constrained informational interactions between “subsystems” of a social system. Dynamic Epistemic Logic provides us with a unifying setting in which these informational interactions, coming from seemingly very different areas of research, can be fully compared and analyzed. The DEL formalism comes with a powerful set of tools that allows us to make the underlying dynamic/interactive mechanisms fully transparent. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)