Boolean algebras of conditionals, probability and logic

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.

KEYWORDS Conditional probability; conditional events; Boolean algebras; preferential consequence relations

T. Flaminio, L. Godo and  H. Hosni. (2020). “Boolean algebras of conditionals, probability and logic” Artificial Intelligence.  doi.org/10.1016/j.artint.2020.103347 (Open Access)

A Fully Rational Account of Structured Argumentation Under Resource Bounds

ASPIC+ is an established general framework for argumentation and non-monotonic reasoning. However ASPIC+ does not satisfy the non-contamination rationality postulates, and moreover, tacitly assumes unbounded resources when demonstrating satisfaction of the consistency postulates. In this paper we present a new version of ASPIC+ – Dialectical ASPIC+ – that is fully rational under resource bounds.

M. D’Agostino and S. Modgil. A Fully Rational Account of Structured Argumentation Under Resource Bounds. Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI-20)

IJCAI, the International Joint Conference on Artificial Intelligence, is the premier conference for the international AI community to communicate the advances and achievements of AI research. 
IJCAI-PRICAI20 received  4717 valid submissions, of which only 592 have been accepted, for a record-low overall acceptance rate of 12.6%.

Depth-Bounded Approximations of Probability

Logica Milano

We introduce measures of uncertainty that are based on Depth-Bounded Logics and resemble belief functions. We show that our measures can be seen as approximation of classical probability measures over classical logic, and that a variant of the PSAT problem for them is solvable in polynomial time.

Baldi P., D’Agostino M., Hosni H. (2020) “Depth-Bounded Approximations of Probability”. In: Lesot MJ. et al. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2020. Communications in Computer and Information Science, vol 1239. Springer, Cham DOI: 10.1007/978-3-030-50153-2_45

Rasmus Rendsvig – Logics for Social Networks

11 June 2020 – 5pm on Teams

In this talk, I will discuss logics for social networks, their epistemic extensions, and dynamics in such structure, including diffusion as modeled by threshold models. I will present a selection of recent models for social networks and their epistemics, with a focus on how these may be represented using dynamic term-modal logic (DTML)—a dynamic, quantified
modal/epistemic logic, where the subscripts of operators are first-order terms, allowing formulas such as $\exist x K_x N(x,b)$: there exists and agent that knows that it is networked with agent b. DTML is based on an enriched version of action models of dynamic epistemic logic fame, and comes with a complete set of reduction axioms. Modelling social network dynamics in DTML thus directly provide sound and complete logics. Additionally, such logics are decidable when only a finite set of agents is considered.

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Rasmus K. Rendsvig is Postdoctoral researcher at the Center for Information and Bubble Studies,University of Copenhagen

Depth-bounded Belief Functions

This paper introduces and investigates Depth-bounded Belief functions, a logic-based representation of quantified uncertainty. Depth-bounded Belief functions are based on the framework of Depth-bounded Boolean logics, which provide a hierarchy of approximations to classical logic. Similarly, Depth-bounded Belief functions give rise to a hierarchy of increasingly tighter lower and upper bounds over classical measures of uncertainty. This has the rather welcome consequence that “higher logical abilities” lead to sharper uncertainty quantification. In particular, our main results identify the conditions under which Dempster-Shafer Belief functions and probability functions can be represented as a limit of a suitable sequence of Depth-bounded Belief functions.

KEYWORDS: Belief functions; Uncertain reasoning; Depth-bounded logics; Probability.

P. Baldi and H. Hosni. (2020). “Depth-bounded Belief FunctionsInternatonal Journal of Approximate Reasoning, Volume 123, August 2020, Pages 26-40. doi.org/10.1016/j.ijar.2020.05.001 (Open Access)

Job Opening

POSTDOCTORAL RESEARCHER IN LOGIC

ProjectFORMAL ARGUMENTATION: A FRAMEWORK FOR RATIONAL REASONING AND LEARNING UNDER UNCERTAINTY IN AI
Duration: 2 years
We are looking for a very strong and highly motivated postdoctoral researcher in Logic to join Marcello D’Agostino and Hykel Hosni who are the PIs of the project “Logical Foundations and Applications of Depth-Bounded Probability”. This project is part of a 5 years “Excellence Scheme” which has been awarded in 2017 to The Department of Philosophy at the University of Milan “La Statale” in recognition of its leading role in research and innovative teaching.
For more information, see here.