Studia Logica

Book Reviews

Introduction to the Special Issue on Logic and the Foundations of Game and Decision Theory (LOFT12)

Book Reviews

The Monodic Fragment of Propositional Term Modal Logic Abstract We study term modal logics, where modalities can be indexed by variables that can be quantified over. We suggest that these logics are appropriate for reasoning about systems of unboundedly many reasoners and define a notion of bisimulation which preserves propositional fragment of term modal logics. Also we show that the propositional fragment is already undecidable but that its monodic fragment (formulas using only one free variable in the scope of a modality) is decidable, and expressive enough to include interesting assertions.

Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks Abstract We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this diffusion policy, threshold models develop dynamically towards a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors' behavior allows agents to anticipate changes in behavior of their closer neighbors. Overall, our logical formalism captures the interplay between the epistemic and social dimensions in social networks.

The Dynamics of Epistemic Attitudes in Resource-Bounded Agents Abstract The paper presents a new logic for reasoning about the formation of beliefs through perception or through inference in non-omniscient resource-bounded agents. The logic distinguishes the concept of explicit belief from the concept of background knowledge. This distinction is reflected in its formal semantics and axiomatics: (i) we use a non-standard semantics putting together a neighborhood semantics for explicit beliefs and relational semantics for background knowledge, and (ii) we have specific axioms in the logic highlighting the relationship between the two concepts. Mental operations of perceptive type and inferential type, having effects on epistemic states of agents, are primitives in the object language of the logic. At the semantic level, they are modelled as special kinds of model-update operations, in the style of dynamic epistemic logic. Results about axiomatization, decidability and complexity for the logic are given in the paper.

Jan von Plato, Saved from the Cellar. Gerhard Gentzen's Shorthand Notes on Logic and the Foundations of Mathematics

Logics for Moderate Belief-Disagreement Between Agents Abstract A moderate belief-disagreement between agents on proposition p means that one agent believes p and the other agent does not. This paper presents two logical systems, \(\mathbf {MD}\) and \(\mathbf {MD}^D\) , that describe moderate belief-disagreement, and shows, using possible worlds semantics, that \(\mathbf {MD}\) is sound and complete with respect to arbitrary frames, and \(\mathbf {MD}^D\) is sound and complete with respect to serial frames. Syntactically, the logics are monomodal, but two doxastic accessibility relations are involved in their semantics. The notion of moderate belief-disagreement, which is in accordance with the understanding of belief-disagreement in everyday life, is an epistemic one related to multiagent situations, and \(\mathbf {MD}\) and \(\mathbf {MD}^D\) are two epistemic logics.

Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic Abstract In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic known as 4CC. These theorems are proved using Schütte's method, which can simultaneously prove completeness and cut-elimination.

Truthmakers and Normative Conflicts Abstract By building on work by Kit Fine, we develop a sound and complete truthmaker semantics for Lou Goble's conflict tolerant deontic logic \(\mathbf {BDL}\) .