Where causality, conditionals and epistemology meet:A logical inquiry

This dissertation is an intellectual journey along topics at the intersection of the study of conditionals, causality and epistemology. It will focus on a couple of problems at this intersection pointed out in recent research. I will demonstrate how by combining knowledge and tools from all three fields we can make substantial progress on solving these issues. I will also show that this integrated approach provides us with a better understanding of the relation between conditionals, causality and epistemology

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

Supervenience, Dependence, Disjunction

This paper explores variations on and connections between the topics mentioned in its title, using as something of an anchor the discussion in Valentin Goranko and Antti Kuusisto’s “Logics for propositional determinacy and independence”, a venture into what the authors call the logic of determinacy, which they contrast with (a demodalized version of) Jouko Väänänen’s modal dependence logic. As they make clear in their discussion, these logics are closely connected with the topics of noncontingency and supervenience. Two opening sections of the present paper address some of these connections, including related earlier logical work by the present author as well as very recent work by Jie Fan. The Väänänen-inspired treatment is presented in a third section, and then, in Sections 4 and 5, as a kind of centerpiece for the discussion, we follow Goranko and Kuusisto in elaborating one principal reason offered for preferring their own approach over that treatment, which concerns some anomalies over the behaviour of disjunction in the latter treatment. Sections 6 and 7 look at dependence and (several different versions of) disjunction in inquisitive logic, especially as presented by Ivano Ciardelli. Section 8 revisits the less formal property-supervenience literature with issues from the first two sections of the paper in mind, and we conclude with a Postscript addressing a further conceptual issue pertaining to the relation between modal and quantificational dependence logics

Modal paraconsistent logic

Dissertação de mestrado integrado em Engenharia FísicaSuperconducting quantum circuits are a promising model for quantum computation, al though their physical implementation faces some adversities due to the hardly unavoidable decoherence of superconducting quantum bits. This problem may be approached from a formal perspective, using logical reasoning to perform software correctness of programs executed in the non-ideal available hardware. This is the motivation for the work devel oped in this dissertation, which is ultimately an attempt to use the formalism of transition systems to design logical tools for the engineering of quantum software. A transition system to capture the possibly unexpected behaviors of quantum circuits needs to consider the phenomena of decoherence as a possible error factor. In this way, we propose a new family of transition systems, the Paraconsistent Labelled Transition Systems (PLTS), to describe processes that may behave differently from what is expected when facing specific contexts. System states are connected through transitions which simultaneously characterize the possibility and impossibility of that being the system’s evolution. This kind of formalism may be used to represent processes whose evolution is impossible to be sharply described and, thus, should be able to cope with inconsistencies, as well as with vagueness or missing information. Besides giving the formal definition of PLTS, we establish how they are related under the notions of morphism, simulation, bisimulation and trace equivalence. It is a common practice to combine transition systems through universal constructions, in a suitable category, which forms a basis for a process description language. In this dis sertation, we define a category of PLTS and propose a number of constructions to combine them, providing a basis for such a language. Transition systems are usually associated with modal logics which provide a formal set ting to express and prove their properties. We also propose a modal logic, more specifically, a modal intuitionistic paraconsistent logic (MIPL), to talk about PLTS and express their properties, studying how the equivalence relations defined for PLTS extend to relations on MIPL models and how the satisfaction of formulas is preserved along related models. Finally, we illustrate how superconducting quantum circuits may be represented by a PLTS and propose the use of PLTS equivalence relations, namely that of trace equivalence, to compare circuit effectiveness.Os circuitos quânticos que operam qubits supercondutores são um modelo promissor para a arquitetura de computadores quânticos. No entanto, a sua implementação física pode tornar-se ineficaz, devido a fenómenos de decoerência a que os qubits em questão estão altamente sujeitos. Uma possível abordagem a este problema consiste em empregar a lógica e as suas ferramentas para a correção de programas a executar nestes dispositivos. A proposta desta dissertação é que se utilize o formalismo dos sistemas de transição para modelar e descrever o comportamento dos circuitos quânticos, que, por vezes, pode ser imprevisível. Para tal, considera-se a decoerência de qubits como um possível fator de erro nas computações. Assim surge uma nova família de sistemas de transição, os Paraconsistent Labelled Transition systems (PLTS), como um modelo para descrever processos que, em determinados contextos, se comportam de forma diferente do que é esperado. Os estados de um PLTS estão conectados por transições que caracterizam, simultaneamente, a possibilidade e a impossibilidade de o sistema evoluir transitando de um estado para o outro. Este é um modelo em que a informação acerca das transições pode ser incompleta ou mesmo contraditória. Além da definição formal dos PLTS, são também sugeridas, como relações entre PLTS, as noções de morfismo, simulação, bissimulação e equivalência por traços. Muitas vezes, os sistemas de transição são combinados através de construções universais numa categoria adequada, de forma a definir uma álgebra de processos. Também neste trabalho é definida uma categoria de PLTS e são propostas algumas construções, típicas nas álgebras de processos, para os combinar. Os sistemas de transição são geralmente associados a lógicas modais, que permitem expressar e provar as suas propriedades. A definição dos PLTS conduziu à definição de uma lógica modal, MIPL, que permitiu determinar de que forma as relações de equivalência definidas para PLTS, e estendidas para modelos da logica MIPL, se refletem na preservação da satisfação de fórmulas sobre os modelos relacionados. Por fim, propõe-se utilizar PLTS para a representação de circuitos quânticos e comparar a eficácia dos circuitos através da relação de equivalência por traços

Achieving while maintaining:A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $\phi$ given $\psi$ while maintaining $\chi$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.Comment: appear in Proceedings of ICLA 201

Contributions of formal language theory to the study of dialogues

For more than 30 years, the problem of providing a formal framework for modeling dialogues has been a topic of great interest for the scientific areas of Linguistics, Philosophy, Cognitive Science, Formal Languages, Software Engineering and Artificial Intelligence. In the beginning the goal was to develop a "conversational computer", an automated system that could engage in a conversation in the same way as humans do. After studies showed the difficulties of achieving this goal Formal Language Theory and Artificial Intelligence have contributed to Dialogue Theory with the study and simulation of machine to machine and human to machine dialogues inspired by Linguistic studies of human interactions. The aim of our thesis is to propose a formal approach for the study of dialogues. Our work is an interdisciplinary one that connects theories and results in Dialogue Theory mainly from Formal Language Theory, but also from another areas like Artificial Intelligence, Linguistics and Multiprogramming. We contribute to Dialogue Theory by introducing a hierarchy of formal frameworks for the definition of protocols for dialogue interaction. Each framework defines a transition system in which dialogue protocols might be uniformly expressed and compared. The frameworks we propose are based on finite state transition systems and Grammar systems from Formal Language Theory and a multi-agent language for the specification of dialogue protocols from Artificial Intelligence. Grammar System Theory is a subfield of Formal Language Theory that studies how several (a finite number) of language defining devices (language processors or grammars) jointly develop a common symbolic environment (a string or a finite set of strings) by the application of language operations (for instance rewriting rules). For the frameworks we propose we study some of their formal properties, we compare their expressiveness, we investigate their practical application in Dialogue Theory and we analyze their connection with theories of human-like conversation from Linguistics. In addition we contribute to Grammar System Theory by proposing a new approach for the verification and derivation of Grammar systems. We analyze possible advantages of interpreting grammars as multiprograms that are susceptible of verification and derivation using the Owicki-Gries logic, a Hoare-based logic from the Multiprogramming field