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Complexity of Model Checking for Inquisitive Propositional and Modal Logic

Core Concepts
Model checking complexity for inquisitive logics is proven to be PSPACE-complete.
The paper studies the complexity of model checking problems for inquisitive propositional logic InqB and modal logic InqM, proving them to be AP-complete. It introduces inquisitive logics, information models, and semantics. The study includes a reduction of the TQBF problem to MC(InqB), establishing PSPACE-completeness. Introduction: Studies model checking complexity for InqB and InqM. Defines inquisitive logics extending classical logic with questions. Preliminaries: Information models defined for InqB and InqM. Semantics based on information states supporting statements/questions. Encoding and Model Checking Algorithm: Switching models used to encode Boolean valuations. Special formulas introduced to encode TQBF problem into MC(InqB). Complexity of Model Checking for InqB: Reduction of TQBF problem to MC(InqB) proves PSPACE-completeness.
In recent years, the problem has been addressed also for a class of logics called team logics which, like our inquisitive systems, are interpreted relative to sets of assignments (see, e.g., [5, 6] and [9, Ch. 7]). Both MC(InqB) and MC(InqM) are PSPACE-complete.

Deeper Inquiries

How do switching models enhance the understanding of Boolean valuations

Switching models enhance the understanding of Boolean valuations by providing a structured framework to represent and interpret them. These models allow us to encode Boolean valuations as information states, where each state corresponds to a specific valuation over a set of atomic propositions. By defining switching models with specific properties related to the atoms and worlds in the model, we can easily map Boolean valuations to these states. This mapping provides a clear correspondence between Boolean truth values and the support of inquisitive formulas on these states.

What implications does the PSPACE-completeness have on practical applications

The PSPACE-completeness of problems like MC(InqB) and MC(InqM) has significant implications for practical applications involving complex logical reasoning tasks. In practical terms, it means that solving these model checking problems requires resources proportional to polynomial space complexity, making them computationally challenging for large-scale systems or scenarios with numerous variables and constraints. The PSPACE-completeness indicates that these problems are among the hardest problems solvable within polynomial space bounds, highlighting their complexity and potential limitations in real-world applications.

How can the concept of information states be extended beyond formal logic

The concept of information states can be extended beyond formal logic into various fields such as artificial intelligence, decision-making processes, knowledge representation systems, and database management. Information states provide a structured way to represent knowledge structures where different pieces of information interact based on certain rules or relationships defined within the system. By extending this concept beyond formal logic, we can create sophisticated models for capturing complex data dependencies, reasoning patterns, uncertainty handling mechanisms, and decision-making strategies across diverse domains ranging from cognitive science to machine learning algorithms.