Reasoning about discrete and continuous noisy sensors and effectors in dynamical systems

Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive. While their formalism is quite general, it is restricted to fluents whose values are drawn from discrete finite domains, as opposed to the continuous domains seen in many robotic applications. In this work, we show how this limitation in that approach can be lifted. By dealing seamlessly with both discrete distributions and continuous densities within a rich theory of action, we provide a very general logical specification of how belief should change after acting and sensing in complex noisy domains.Comment: To appear in Artificial Intelligence 201

The Logical and Philosophical Foundations for the Possibility of True Contradictions

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true. Rather than advocating the truth of certain contradictions, this thesis offers a different challenge to the classical logician. By showing that it can be philosophically coherent to propose that true contradictions are metaphysically possible, the thesis suggests that the classical logician must do more than she currently has to justify her confidence in the impossibility of true contradictions. Simply fighting off the dialetheist’s putative examples of true contradictions at the actual world isn’t enough to justify the classical logician’s conclusion that true contradictions are impossible. To aid the thesis dialectically, we introduce a new position, absolutism, which hypothesises that it’s metaphysically possible for at least one contradiction to be true, contrasting with the dialetheic hypothesis that some contradictions are true in the actual world. We demonstrate that absolutism can be given a philosophically coherent interpretation, an appropriate logic, and that certain criticisms are completely toothless against absolutism. The challenge put to the classical logician is then: On what logical or philosophical grounds can we rule out the metaphysical possibility of true contradictions

The logical and philosophical foundations for the possibility of true contradictions

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true. Rather than advocating the truth of certain contradictions, this thesis offers a different challenge to the classical logician. By showing that it can be philosophically coherent to propose that true contradictions are metaphysically possible, the thesis suggests that the classical logician must do more than she currently has to justify her confidence in the impossibility of true contradictions. Simply fighting off the dialetheist’s putative examples of true contradictions at the actual world isn’t enough to justify the classical logician’s conclusion that true contradictions are impossible. To aid the thesis dialectically, we introduce a new position, absolutism, which hypothesises that it’s metaphysically possible for at least one contradiction to be true, contrasting with the dialetheic hypothesis that some contradictions are true in the actual world. We demonstrate that absolutism can be given a philosophically coherent interpretation, an appropriate logic, and that certain criticisms are completely toothless against absolutism. The challenge put to the classical logician is then: On what logical or philosophical grounds can we rule out the metaphysical possibility of true contradictions

Creationism and evolution

In Tower of Babel, Robert Pennock wrote that “defenders of evolution would help their case immeasurably if they would reassure their audience that morality, purpose, and meaning are not lost by accepting the truth of evolution.” We first consider the thesis that the creationists’ movement exploits moral concerns to spread its ideas against the theory of evolution. We analyze their arguments and possible reasons why they are easily accepted. Creationists usually employ two contradictive strategies to expose the purported moral degradation that comes with accepting the theory of evolution. On the one hand they claim that evolutionary theory is immoral. On the other hand creationists think of evolutionary theory as amoral. Both objections come naturally in a monotheistic view. But we can find similar conclusions about the supposed moral aspects of evolution in non-religiously inspired discussions. Meanwhile, the creationism-evolution debate mainly focuses — understandably — on what constitutes good science. We consider the need for moral reassurance and analyze reassuring arguments from philosophers. Philosophers may stress that science does not prescribe and is therefore not immoral, but this reaction opens the door for the objection of amorality that evolution — as a naturalistic world view at least — supposedly endorses. We consider that the topic of morality and its relation to the acceptance of evolution may need more empirical research

Worlds and Objects of Epistemic Space : A study of Jaakko Hintikka's modal semantics

This study focuses on meaning and knowledge by assessing a distinctive view regarding their relation, namely the modal view of Jaakko Hintikka. The development of this view has not been previously scrutinized. By paying close attention to the texts of Hintikka, I show that, despite the extensive deployment of mathematical tools, the articulation of the view remained intuitive and vague. The study calls attention to several points at which Hintikka omits relevant details or disregards foundational questions. Attempts are made to articulate Hintikka’s certain ideas in a more specific manner, and new problems that result are identified. The central claim argued for is that Hintikka’s exposition was unsatisfactory in many respects and hence the view, as it stands, falls short in its explanatory scope compared to current theories in the intersection of logic, semantics, and epistemology. However, I argue that, despite its shortcomings, the prospects of the modal view are not exhausted. This is verified by introducing a new interpretation of the framework and by sketching new applications relevant in philosophy of language and in epistemology. It is also pointed out that certain early advances of the view closely resemble, and therefore anticipate, the central tenets of the currently influential two-dimensional approaches in logic and semantics.Tutkimus paneutuu merkityksen ja tiedon käsitteisiin tarkastelemalla Jaakko Hintikan työtä modaalisen semantiikan parissa. Tutkimus osoittaa, että Hintikka jätti modaalisen semantiikan kehitystyössään avoimeksi useita perustavia kysymyksiä ja yksityiskohtia. Tutkimuksessa pyritään artikuloimaan täsmällisemmin joitakin Hintikan näkemyksiä, ja tunnistetaan uusia syntyviä ongelmia. Keskeisenä väitteenä on, että Hintikan teoreettinen työ jäi monilta osin epätyydyttäväksi, ja siten hänen modaalinen näkemyksensä ei yllä selitysvoimaltaan ja sovelluspotentiaaliltaan samalle tasolle kuin nykyiset filosofiset teoriat, jotka operoivat logiikan, semantiikan ja epistemologian risteyskohdissa. Tästä huolimatta tutkimuksessa argumentoidaan, että Hintikan teoreettinen viitekehys tarjoaa myös uusia kiinnostavia näköaloja. Tämä todennetaan tarjoamalla Hintikan viitekehykselle uusi tulkinta, ja soveltamalla sitä uusiin kielifilosofisiin kysymyksiin. Tutkimus nostaa myös esiin kirjallisuudessa ohitetun tosiasian, että Hintikan työ ennakoi tärkeällä tavalla nykyisin vaikutusvaltaisia kaksi-dimensionaalisia lähestymistapoja logiikassa ja semantiikassa

Proof theoretic criteria for logical constancy

Logic concerns inference, and some inferences can be distinguished from others by their holding as a matter of logic itself, rather than say empirical factors. These inferences are known as logical consequences and have a special status due to the strong level of confidence they inspire. Given this importance, this dissertation investigates a method of separating the logical from the non-logical. The method used is based on proof theory, and builds on the work of Prawitz, Dummett and Read. Requirements for logicality are developed based on a literature review of common philosophical use of the term, with the key factors being formality, and the absolute generality / topic neutrality of interpretations of logical constants. These requirements are used to generate natural deduction criteria for logical constancy, resulting in the classification of certain predicates, truth functional propositional operators, first order quantifiers, second order quantifiers in sound and complete formal systems using Henkin semantics, and modal operators from the systems K and S5 as logical constants. Semantic tableaux proof systems are also investigated, resulting in the production of semantic tableaux-based criteria for logicality

Modal Action Logics for Reasoning about Reactive Systems

Meyer, J-.J.Ch. [Promotor]Riet, R.P. [Promotor]van de Wieringa, R. [Promotor