The Journal of Applied Logic’s latest issue features two new papers by some of our group members. You can easily access them at this link.
M. D’Agostino, C. Larese and S. Modgil – Towards Depth-bounded Natural Deduction for Classical First-order Logic
Abstract: In this paper we lay the foundations of a new proof-theory for classical first-order logic that allows for a natural characterization of a notion of inferential depth. The approach we propose here aims towards extending the proof-theoretical framework presented in  by combining it with some ideas inspired by Hintikka’s work . Unlike standard natural deduction, in this framework the inference rules that fix the meaning of the logical operators are symmetrical with respect to assent and dissent and do not involve the discharge of formulas. The only discharge rule is a classical dilemma rule whose nested applications provide a sensible measure of inferential depth. The result is a hierarchy of decidable depth-bounded approximations of classical first-order logic that expands the hierarchy of tractable approximations of Boolean logic investigated in [11, 10, 7].
M. Fait and G. Primiero – HTLC: Hyperintensional Typed Lambda Calculus
Abstract: In this paper we introduce the logic HTLC, for Hyperintensional Typed Lambda Calculus. The system extends the typed λ-calculus with hyperintensions and related rules. The polymorphic nature of the system allows to reason with expressions for extensional, intensional and hyperintentsional entities. We inspect meta-theoretical properties and show that HTLC is complete in Henkin’s sense under a weakening of the cardinality constraint for the domain of hyperintensions.
Recent developments in the formalization of reasoning, especially in computational settings, have aimed at defining cognitive and resource bounds to express limited inferential abilities. This feature is emphasized by Depth Bounded Boolean Logics, an informational logic that models epistemic agents with inferential abilities bounded by the amount of information they can use. However, such logics do not model the ability of agents to make use of information shared by other sources. The present paper provides a first account of a Multi-Agent Depth Bounded Boolean Logic, defining agents whose limited inferential abilities can be increased through a dynamic operation of becoming informed by other data sources.
KEYWORDS: Logic of information, Resource bounded reasoning, Information transmission
The role of misinformation diffusion during a pandemic is crucial. An aspect that requires particular attention in the analysis of misinfodemics is the rationale of the source of false information, in particular how the behavior of agents spreading misinformation through traditional communication outlets and social networks can influence the diffusion of the disease. We studied the process of false information transmission by malicious agents, in the context of a disease pandemic based on data for the COVID-19 emergency in Italy. We model communication of misinformation based on a negative trust relation, supported by findings in the literature that relate the endorsement of conspiracy theories with low trust level towards institutions. We provide an agent-based simulation and consider the effects of a misinfodemic on policies related to lockdown strategies, isolation, protection and distancing measures, and overall negative impact on society during a pandemic. Our analysis shows that there is a clear impact by misinfodemics in aggravating the results of a current pandemic.
KEYWORDS Misinformation, Misinfodemics, Multi-Agent Systems
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.
We present a logic to model the behaviour of an agent trusting or not trusting messages sent by another agent. The logic formalizes trust as a consistency checking function with respect to currently available information. Negative trust is modeled in two forms: distrust as the rejection of incoming inconsistent information; mistrust, as revision of previously held information becoming undesirable in view of new incoming inconsistent information, which the agent wishes to accept. We provide a natural deduction calculus, a relational semantics and prove soundness and completeness results. We overview a number of applications which have been investigated for the proof-theoretical formulation of the logic.
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.
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.