相关论文: PSPACE Reasoning for Graded Modal Logics

For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal…

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…

The methods used to establish PSPACE-bounds for modal logics can roughly be grouped into two classes: syntax driven methods establish that exhaustive proof search can be performed in polynomial space whereas semantic approaches directly…

We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of…

It is known that many modal and superintuitionistic logics are PSPACE-hard in languages with a small number of variables; however, questions about the complexity of similar fragments of many logics obtained by adding various axioms to…

We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem…

Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…

We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…

It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators,…

By using a selective filtration argument, we prove that the satisfiability problem of the unimodal logic of density is in $EXPTIME$. By using a tableau-like approach, we prove that the satisfiability problem of the bimodal logic of weak…

The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…

We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…

Windows have been introduce in \cite{BalGasq25} as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the ``folklore'' case of bimodal $\K4$ already treated…

Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…

In a recently launched research program for developing logic as a formal theory of (interactive) computability, several very interesting logics have been introduced and axiomatized. These fragments of the larger Computability Logic aim not…

Exact tight bounds of the complexity of the satisfiability problem for dense modal logics is a difficult question, likely somewhere between $\PSPACE$ and $\EXPSPACE$ depending of the logic under question. For a class of them, called here…

In real-world applications of reinforcement learning (RL), noise from inherent stochasticity of environments is inevitable. However, current policy evaluation algorithms, which plays a key role in many RL algorithms, are either prone to…

We consider the operation of sum on Kripke frames, where a family of frames-summands is indexed by elements of another frame. In many cases, the modal logic of sums inherits the finite model property and decidability from the modal logic of…

Probabilistic justification logic is a modal logic with two kind of modalities: probability measures and explicit justification terms. We present a tableau procedure that can be used to decide the satisfiability problem for this logic in…

Refinement Modal Logic (RML), which was recently introduced by Bozzelli et al., is an extension of classical modal logic which allows one to reason about a changing model. In this paper we study computational complexity questions related to…