Final Report Summary - WADOXA (Ways of Doxastic Agency: Information Update, Belief Formation and Assessment of Conduct.)
The technical target of my work with the WADOXA project was to merge two different formal frameworks: the DEL (Dynamic Epistemic Logic) framework and the STIT (Seeing-to-it-that) framework. The first captures the beliefs or knowledge of individuals and groups and how new information (be it true or false) may change it. The second captures how agents and group secures outcome by making choices. The conceptual target was of the project was to provide a rigorous tool for modeling those cases of action that are prompted by the release of information. I summarize the work that I have carried in order to fulfil these goals, with reference to the specific research objectives detailed by the WADOXA project.
In order to fulfil Research Objective 1 (section B4.3 of my Marie Curie application), I have identified the mathematical tools that allow for an optimal combination of features of the STIT and DEL framework. This is in turn essential to design adequate DEL-STIT models. These tools consist of (1) a special kind of action models from the DEL-tradition, that account for change in the world (ontic change) beside change in the agents’ information; (2) flat STIT models encoding no temporal distinctions; (3) a condition of independence over global actions. Also, I have integrated the mathematical tool with a language displaying both dynamic operators for events and modal operators for agency. The language results from the combination of one language from the DEL tradition and one from the STIT tradition.
In order to fulfil Research Objective 3, I have designed a formalism combining dynamics and universal modality, in order to express ‘alternate doxastic agency’. This is turn is essential to reason about what agents would decide, if they believed or knew otherwise. This formalism combines (1) a special knowledge operator that is interpreted on perfect-information strategic games and captures the notion of ex interim knowledge from Game Theory and (2) an update operator for disclosure of hard information. With this at hand, we can express what an agent would decide had she known otherwise.
I have designed a belief operator alongside the ex interim knowledge operator. The belief operator is interpreted on mathematical structures known as connected preorders. These structures are integrated with equivalence classes, to the effect that an agent believes whatever she knows ex interim. The structure is completed by a function transforming the preorders and changing the agents’ beliefs accordingly. This fulfills Research Objective 2.
Due to early interruption of the fellowship on May 31, 2016, I did not go through Research Objective 4.
As for the training activities, I have made extensive use of training possibilities offered by the ILLC. I have attended the courses on Logic, Knowledge and Science by Prof. Smets and Dynamic Epistemic Logic by Prof. Baltag, as specified in section B2.2 of my application. Also, I have attended one course on Game Theory by Dr. Valerio Capraro.
Attendance to a course in Game Theory was not planned by the WADOXA proposal, but it was urged by the need to acquire a solid theoretical framework for decision-making and strategic interaction of different agents. In the development of the project, strategic reasoning and rationality have assumed increasing importance, since they allow for a deeper understanding of decision-making under uncertainty, especially when many different agents play a role, as in the paradigmatic cases inspiring the WADOXA proposal.
The courses I attended proved an excellent introduction to the formal aspects of epistemic logic, information and belief change, and strategic interaction. These are in turn crucial areas of research in the scientific community where I want to establish myself as an all-round international researcher.
Additionally, I was a regular attendee at the LiRA seminar organized by the Amsterdam Dynamics Group from the ILLC, focusing mainly on information change, belief revision, rationality and strategic interaction. Courses and seminars helped me enhance my knowledge in key areas of interest – in particular, epistemic foundations of Game Theory and logics for rational interaction – by providing relevant background, techniques and research perspectives in these areas. I have also received excellent support from my supervisor, Prof. Alexandru Baltag, which allowed me to progress towards my training objectives of acquiring strong qualitative research skills.
These training activities have been very important for my research and professional development, and they helped me develop research skills in the mathematical theories of information change (Dynamic Epistemic Logic and Belief Revision) that were a central objective in my WADOXA proposal (section B2.2).
As envisaged in the WADOXA proposal, I have also taught two short project-courses in logics for decision-making and deontic logic. These are one-month research-oriented courses that are offered by the ILLC on a proposal by the lecturer. I have taught an Introduction to STIT logic on June 2015, in order to disseminate knowledge on my area of specialization (modal logic of agency and consequentialist reasoning on decision-making) and a course on Contrary-to-Duty Obligations in January 2016, in order to target problems where the responsibility of individuals is conditional on a given background of facts.
I have also joined three different MA committees as an expert in the topics in question, which got me acquainted with an important aspect of departmental activities and has improved my ability to assess research by others. Progress in my teaching, supervising, and valuation skills is crucial for my next career move within academia.
In order to fulfil Research Objective 1 (section B4.3 of my Marie Curie application), I have identified the mathematical tools that allow for an optimal combination of features of the STIT and DEL framework. This is in turn essential to design adequate DEL-STIT models. These tools consist of (1) a special kind of action models from the DEL-tradition, that account for change in the world (ontic change) beside change in the agents’ information; (2) flat STIT models encoding no temporal distinctions; (3) a condition of independence over global actions. Also, I have integrated the mathematical tool with a language displaying both dynamic operators for events and modal operators for agency. The language results from the combination of one language from the DEL tradition and one from the STIT tradition.
In order to fulfil Research Objective 3, I have designed a formalism combining dynamics and universal modality, in order to express ‘alternate doxastic agency’. This is turn is essential to reason about what agents would decide, if they believed or knew otherwise. This formalism combines (1) a special knowledge operator that is interpreted on perfect-information strategic games and captures the notion of ex interim knowledge from Game Theory and (2) an update operator for disclosure of hard information. With this at hand, we can express what an agent would decide had she known otherwise.
I have designed a belief operator alongside the ex interim knowledge operator. The belief operator is interpreted on mathematical structures known as connected preorders. These structures are integrated with equivalence classes, to the effect that an agent believes whatever she knows ex interim. The structure is completed by a function transforming the preorders and changing the agents’ beliefs accordingly. This fulfills Research Objective 2.
Due to early interruption of the fellowship on May 31, 2016, I did not go through Research Objective 4.
As for the training activities, I have made extensive use of training possibilities offered by the ILLC. I have attended the courses on Logic, Knowledge and Science by Prof. Smets and Dynamic Epistemic Logic by Prof. Baltag, as specified in section B2.2 of my application. Also, I have attended one course on Game Theory by Dr. Valerio Capraro.
Attendance to a course in Game Theory was not planned by the WADOXA proposal, but it was urged by the need to acquire a solid theoretical framework for decision-making and strategic interaction of different agents. In the development of the project, strategic reasoning and rationality have assumed increasing importance, since they allow for a deeper understanding of decision-making under uncertainty, especially when many different agents play a role, as in the paradigmatic cases inspiring the WADOXA proposal.
The courses I attended proved an excellent introduction to the formal aspects of epistemic logic, information and belief change, and strategic interaction. These are in turn crucial areas of research in the scientific community where I want to establish myself as an all-round international researcher.
Additionally, I was a regular attendee at the LiRA seminar organized by the Amsterdam Dynamics Group from the ILLC, focusing mainly on information change, belief revision, rationality and strategic interaction. Courses and seminars helped me enhance my knowledge in key areas of interest – in particular, epistemic foundations of Game Theory and logics for rational interaction – by providing relevant background, techniques and research perspectives in these areas. I have also received excellent support from my supervisor, Prof. Alexandru Baltag, which allowed me to progress towards my training objectives of acquiring strong qualitative research skills.
These training activities have been very important for my research and professional development, and they helped me develop research skills in the mathematical theories of information change (Dynamic Epistemic Logic and Belief Revision) that were a central objective in my WADOXA proposal (section B2.2).
As envisaged in the WADOXA proposal, I have also taught two short project-courses in logics for decision-making and deontic logic. These are one-month research-oriented courses that are offered by the ILLC on a proposal by the lecturer. I have taught an Introduction to STIT logic on June 2015, in order to disseminate knowledge on my area of specialization (modal logic of agency and consequentialist reasoning on decision-making) and a course on Contrary-to-Duty Obligations in January 2016, in order to target problems where the responsibility of individuals is conditional on a given background of facts.
I have also joined three different MA committees as an expert in the topics in question, which got me acquainted with an important aspect of departmental activities and has improved my ability to assess research by others. Progress in my teaching, supervising, and valuation skills is crucial for my next career move within academia.