Interactive and common knowledge in the state-space model

This paper deals with the prevailing formal model for knowledge in contemporary economics, namely the state-space model introduced by Robert Aumann in 1976. In particular, the paper addresses the following question arising in this formalism: in order to state that an event is interactively or commonly known among a group of agents, do we need to assume that each of them knows how the information is imparted to the others? Aumann answered in the negative, but his arguments apply only to canonical, i.e., completely specified state spaces, while in most applications the state space is not canonical. This paper addresses the same question along original lines, demonstrating that the answer is negative for both canonical and not-canonical state spaces. Further, it shows that this result ensues from two counterintuitive properties held by knowledge in the state-space model, namely Substitutivity and Monotonicity.

Maps of Bounded Rationality

The work cited by the Nobel committee was done jointly with the late Amos Tversky (1937-1996) during a long and unusually close collaboration. Together, we explored the psychology of intuitive beliefs and choices and examined their bounded rationality. This essay presents a current perspective on the three major topics of our joint work: heuristics of judgment, risky choice, and framing effects. In all three domains we studied intuitions - thoughts and preferences that come to mind quickly and without much reflection. I review the older research and some recent developments in light of two ideas that have become central to social-cognitive psychology in the intervening decades: the notion that thoughts differ in a dimension of accessibility - some come to mind much more easily than others - and the distinction between intuitive and deliberate thought processes.behavioral economics; experimental economics

From Probabilistic Programming to Complexity-based Programming

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms proposed by Simplicity Theory, relying on the computation of two Kolmogorov complexities (here implemented as min-path searches via ASP programs) rather than probabilistic inference. The proposed system enables users to compute ex-post and ex-ante measures of unexpectedness of a certain situation, mapping respectively to posterior and prior subjective probabilities. The computation is based on the specification of world and mental models by means of causal and descriptive relations between predicates weighted by complexity. The paper illustrates a few examples of application: generating relevant descriptions, and providing alternative approaches to disjunction and to negation

Accounting for Framing-Effects - an informational approach to intensionality in the Bolker-Jeffrey decision model

We suscribe to an account of framing-effects in decision theory in terms of an inference to a background informationa by the hearer when a speaker uses a certain frame while other equivalent frames were also available. This account was sketched by Craig McKenzie. We embed it in Bolker-Jeffrey decision model (or logic of action) - one main reason of this is that this latter model makes preferences bear on propositions. We can deduce a given anomaly or cognitive bias (namely framing-effects) in a formal decision theory. This leads to some philosophical considerations on the relationship between the rationality of preferences and the sensitivity to descriptions or labels of states of affairs (intensionality) in decision-making.information-processing and decision-making, framing-effects, intensionality, Bolker-Jeffrey

The Intrinsic Structure of Quantum Mechanics

The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: (1) it does not refer to any abstract mathematical objects, (2) it is free from the usual arbitrary conventions, and (3) it explains why the wave function has its gauge degrees of freedom, something that are usually put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to "wave function realism.

Verovatnosno zaključivanje u izračunavanju i teoriji funkcionalnih tipova

This thesis investigates two different approaches for probabilistic reasoning in models of computation. The most usual approach is to extend the language of untyped lambda calculus with probabilistic choice operator which results in probabilistic computation. This approach has shown to be very useful and applicable in various fields, e.g. robotics, natural language processing, and machine learning. Another approach is to extend the language of a typed lambda calculus with probability operators and to obtain a framework for probabilistic reasoning about the typed calculus in the style of probability logic. First, we study the lazy call-by-name probabilistic lambda calculus extended with let-in operator, and program equivalence in the calculus. Since the proof of context equivalence is quite challenging, we investigate some effective methods for proving the program equivalence. Probabilistic applicative bisimilarity has proved to be a suitable tool for proving the context equivalence in probabilistic setting. We prove that the probabilistic applicative bisimilarity is fully abstract with respect to the context equivalence in the probabilistic lambda calculus with let-in operator. Next, we introduce Kripke-style semantics for the full simply typed combinatory logic, that is, the simply typed combinatory logic extended with product types, sum types, empty type and unit type. The Kripke-style semantics is defined as a Kripke applicative structure, which is extensional and has special elements corresponding to basic combinators, provided with the valuation of term variables. We prove that the full simply typed combinatory logic is sound and complete with respect to the proposed semantics. We introduce the logic of combinatory logic, that is, a propositional extension of the simply typed combinatory logic. We prove that the axiomatization of the logic of combinatory logic is sound and strongly complete with respect to the proposed semantics. In addition, we prove that the proposed semantics is the new semantics for the simply typed combinatory logic containing the typing rule that ensures that equal terms inhabit the same type. Finally, we introduce the probabilistic extension of the logic of combinatory logic. We extend the logic of combinatory logic with probability operators and obtain a framework for probabilistic reasoning about typed combinatory terms. We prove that the given axiomatization of the logic is sound and strongly complete with respect to the proposed semantics.Теза истражује два различита приступа за вероватносно закључивање у моделима израчунавања. Најчешћи приступ се састоји у проширењу ламбда рачуна вероватносним оператором избора што резултира вероватносним израчунавањем. То се показало веома корисним и примењивим у разним областима, на пример у роботици, обради природног језика и машинском учењу. Други приступ јесте да проширимо језик рачуна вероватносним операторима и добијемо модел за вероватносно закључивање о типизираном рачуну у стилу вероватносне логике. Најпре проучавамо вероватносни ламбда рачун проширен лет-ин оператором где је примењена лења позив-по-имену стратегија евалуације, и изучавамо проблем еквиваленције програма у овом окружењу. Како је проблем доказивања контекстне еквиваленције доста изазован, истраживали смо ефикасне методе за доказивање еквиваленције програма. Вероватносна апликативна бисимулација се показала као одговарајући алат за доказивање еквиваленције програма у вероватносном окружењу. Доказујемо да је вероватносна апликативна бисимулација потпуно апстрактна у односу на контекстну еквиваленцију у вероватносном ламбда рачуну са лет-ин оператором. Затим уводимо Крипкеову семантику за целу комбинаторну логику са функционалним типовима, односно комбинаторну логику са функционалним типовима проширену типовима производа, типовима суме, празним типом и јединичним типом. Крипкеову семантику дефинишемо као Крипкеову апликативну структуру, која је екстензионална и има елементе који одговарају основним комбинаторима, и којој је придружена валуација променљивих. Доказујемо да је цела комбинаторна логика са функционалним типовима сагласна и потпуна у односу на уведене семантике. Уводимо логику комбинаторне логике, то јест исказно проширење комбинаторне логике са функционалним типовима. Доказујемо да је аксиоматизација логике комбинаторне логике сагласна и потпуна у односу на предложену семантику. Даље, показујемо да је уведена семантика нова семантика за комбинаторну логику са функционалним типовима проширену правилом типизирања које осигурава да једнаки терми имају исти тип. На крају, уводимо вероватносно проширење логике комбинаторне логике. Логику комбинаторне логике смо проширили са вероватносним операторима и добили модел за вероватносно закључивање о типизираним комбинаторним термима. Показујемо да је аксиоматизација логике сагласна и јако потпуна у односу на предложену семантику.Teza istražuje dva različita pristupa za verovatnosno zaključivanje u modelima izračunavanja. Najčešći pristup se sastoji u proširenju lambda računa verovatnosnim operatorom izbora što rezultira verovatnosnim izračunavanjem. To se pokazalo veoma korisnim i primenjivim u raznim oblastima, na primer u robotici, obradi prirodnog jezika i mašinskom učenju. Drugi pristup jeste da proširimo jezik računa verovatnosnim operatorima i dobijemo model za verovatnosno zaključivanje o tipiziranom računu u stilu verovatnosne logike. Najpre proučavamo verovatnosni lambda račun proširen let-in operatorom gde je primenjena lenja poziv-po-imenu strategija evaluacije, i izučavamo problem ekvivalencije programa u ovom okruženju. Kako je problem dokazivanja kontekstne ekvivalencije dosta izazovan, istraživali smo efikasne metode za dokazivanje ekvivalencije programa. Verovatnosna aplikativna bisimulacija se pokazala kao odgovarajući alat za dokazivanje ekvivalencije programa u verovatnosnom okruženju. Dokazujemo da je verovatnosna aplikativna bisimulacija potpuno apstraktna u odnosu na kontekstnu ekvivalenciju u verovatnosnom lambda računu sa let-in operatorom. Zatim uvodimo Kripkeovu semantiku za celu kombinatornu logiku sa funkcionalnim tipovima, odnosno kombinatornu logiku sa funkcionalnim tipovima proširenu tipovima proizvoda, tipovima sume, praznim tipom i jediničnim tipom. Kripkeovu semantiku definišemo kao Kripkeovu aplikativnu strukturu, koja je ekstenzionalna i ima elemente koji odgovaraju osnovnim kombinatorima, i kojoj je pridružena valuacija promenljivih. Dokazujemo da je cela kombinatorna logika sa funkcionalnim tipovima saglasna i potpuna u odnosu na uvedene semantike. Uvodimo logiku kombinatorne logike, to jest iskazno proširenje kombinatorne logike sa funkcionalnim tipovima. Dokazujemo da je aksiomatizacija logike kombinatorne logike saglasna i potpuna u odnosu na predloženu semantiku. Dalje, pokazujemo da je uvedena semantika nova semantika za kombinatornu logiku sa funkcionalnim tipovima proširenu pravilom tipiziranja koje osigurava da jednaki termi imaju isti tip. Na kraju, uvodimo verovatnosno proširenje logike kombinatorne logike. Logiku kombinatorne logike smo proširili sa verovatnosnim operatorima i dobili model za verovatnosno zaključivanje o tipiziranim kombinatornim termima. Pokazujemo da je aksiomatizacija logike saglasna i jako potpuna u odnosu na predloženu semantiku

Estruturas lógico-quânticas para partículas semelhantes

In this work we discuss logical structures related to indistinguishable (or similar) particles. Most of the framework used to develop these structures was presented in previous works. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of similar particles, and draw possible philosophical implications. We also review some proposals available in the literature which may be considered within the framework of the quantum logical tradition regarding the problem of indistinguishability. Besides these discussions and constructions, we advance novel technical results, namely, a latticetheoretical structure for identical particles for the finite dimensional case. This approach has not been present in the scarce literature on quantum logic and similar particles.Neste trabalho discutimos estruturas lógicas relacionadas a partículas indistinguíveis (ou semelhantes). A maior parte do quadro teórico usado para desenvolver essas estruturas foi apresentada em trabalhos anteriores. Usamos essas estruturas e construções para discutir possíveis ontologias para partículas idênticas. Em outras palavras, usamos essas estruturas para caracterizar a estrutura lógica de sistemas quânticos para o caso de partículas semelhantes, e traçamos possíveis implicações filosóficas. Também examinamos algumas propostas disponíveis na literatura que podem ser consideradas dentro do quadro da tradição da lógica quântica concernentes ao problema da indistinguibilidade. Além dessas discussões e construções, apresentamos novos resultados técnicos relativos à estrutura da teoria de reticulado para partículas idênticas, no caso de dimensão finita. Esta abordagem não está presente na pequena literatura sobre lógica quântica e partículas semelhantes.Fil: Holik, Federico Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Gomez, Ignacio Sebastián. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaFil: Krause, Décio. Universidade Federal de Santa Catarina; Brasi