Journal of Logic and Computation

Alfano, Gianvincenzo; Greco, Sergio; Parisi, Francesco; Trubitsyna, Irina

doi: 10.1093/logcom/exag025pmid: N/A

Dung’s abstract argumentation framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning. Several research studies have been conducted to expand AF to encompass various aspects, such as the representation of (unquantified) uncertainty, that give rise to the so-called incomplete AF (iAF), where some of the arguments and attacks may be uncertain. In this paper, we introduce three new reasoning problems named totality, determinism and functionality, and investigate their computational complexity for both AF and iAF under several semantics. Intuitively, an argument is said to be deterministic if all extensions assign the same status (either accepted, rejected or undefined) to it, whereas it is said to be total if for all extensions it is either accepted or rejected. When both totality and determinism hold for a given argument, we say that it is functional. We also investigate the complexity of credulous and skeptical acceptance in iAF under semi-stable semantics—a problem left open in the literature. We then show that any iAF can be rewritten into an equivalent one where either only (unattacked) arguments or only attacks are uncertain.

Takahashi, Tenyo

doi: 10.1093/logcom/exag023pmid: N/A

We generalize the theory of stable canonical rules by adopting definable filtration, a generalization of the method of filtration. We show that for a modal rule system or a modal logic that admits definable filtration, each extension is axiomatizable by stable canonical rules. Moreover, we provide an algebraic presentation of Gabbay’s filtration and generalize stable canonical formulas and the axiomatization results via stable canonical formulas for $\textsf{K4}$ to pre-transitive logics $\textsf{K4}^{\textsf{m+1}}_{\textsf{1}} = \textsf{K} + \Diamond ^{m+1} p \to \Diamond p$  $(m \geq 1)$. As consequences, we obtain the finite model property of $\textsf{K4}^{\textsf{m+1}}_{\textsf{1}}$-stable logics and a characterization of splitting and union-splitting logics in the lattice $\textsf{NExt} \textsf{K4}^{\textsf{m+1}}_{\textsf{1}}$. There are continuum many $\textsf{K4}^{\textsf{m+1}}_{\textsf{1}}$-stable logics that are neither $\textsf{K4}$-stable logics nor subframe logics. Finally, we introduce $m$-stable canonical formulas, strengthening the axiomatization results for these logics.1

Wang, Shuangmei; Sun, Fengjie

doi: 10.1093/logcom/exag016pmid: N/A

We study announcement synthesis under incomplete initial beliefs for multiple agents, instantiated with Dalal’s distance-based AGM revision. We introduce and formalize two semantics for the limited-knowledge propositional announcement problem: an optimistic variant (PAP$^{\exists }_{*_{D}}$), which requires success under some admissible completion per agent, and a robust variant (PAP$^{\forall }_{*_{D}}$), which requires success under all admissible completions. This distinction captures a fundamental trade-off in multi-agent coordination: optimism assumes favourable conditions, while robustness hedges against all contingencies. Our first contribution is a tight complexity classification revealing a precise quantifier-complexity correspondence: PAP$^{\exists }_{*_{D}}$ is $\varSigma _{2}^{\rm P}$-complete, while PAP$^{\forall }_{*_{D}}$ is $\varSigma _{3}^{\rm P}$-complete under extensional completion sets. The one-level gap confirms that robustness costs exactly one quantifier alternation in the polynomial hierarchy. The upper bounds follow from a small-announcement normal form—showing that effective coordination messages have bounded complexity—and NP-decidability of the distance-threshold predicate $\mathsf{Dist}_{\le }$. Second, we develop a parameterized tractability landscape that identifies when and why announcement synthesis becomes feasible despite worst-case intractability. We establish FPT algorithms parameterized by vocabulary size $k$ and announcement width $t$; FPT results for bounded completion-set sizes; and FPT in structural parameters (treewidth, backdoor size) via dynamic programming. The bounded-change variant is FPT in the $\ell _{1}$-budget $D=\sum _{i} d_{i}$. Five polynomial-time kernelization rules enable effective preprocessing. Conditional lower bounds under ETH and SETH identify unavoidable exponential dependencies. Finally, we discuss how alternative distance aggregations (average, maximum, Hausdorff) affect computational complexity, showing that our minimum-based framework provides the foundational ‘base case’ upon which more complex variants can build.

Nishimura, Yuki

doi: 10.1093/logcom/exag024pmid: N/A

Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which are essential to treat partial orders. We present terminating tableau calculi complete with respect to some classes of models whose accessibility relations are strictly partially ordered, unbounded strictly partially ordered, partially ordered, strictly totally ordered and totally ordered.

Dvurečenskij, Anatolij; Zahiri, Omid

doi: 10.1093/logcom/exag022pmid: N/A

We investigate nodes (elements that are comparable with all other elements) and their role in the structural analysis of pseudo-hoops. First, we study idempotent nodes and present a complete representation of pseudo-hoops with finitely many idempotent nodes, based on their decomposition into ordinal sums of pseudo-hoops. Next, we examine ordinal sum irreducible pseudo-hoops and prove that every Wajsberg pseudo-hoop with a non-trivial node is linearly ordered. Moreover, we show that the set of nodes $\text{Nod}(\mathbf E)$ of the ordinal sum of any family of Wajsberg pseudo-hoops forms a subalgebra. We then use the set of regular elements of a bounded representable pseudo-hoop $\mathbf E$ and its relationship with $\text{Nod}(\mathbf E)$ to determine whether $\mathbf E$ is ordinal sum reducible or irreducible. As a consequence, we establish that every finite basic pseudo-hoop can be expressed as an ordinal sum of a finite family ${\mathbf E_{1},\ldots ,\mathbf E_{n}}$ for some $n\in \mathbb N$, where $\mathbf E_{1},\ldots ,\mathbf E_{n-1}$ are linear Wajsberg pseudo-hoops and $\mathbf E_{n}$ is ordinal sum irreducible.

de Groot, Jim

doi: 10.1093/logcom/exag017pmid: N/A

We introduce a monotone modal analogue of the intuitionistic (normal) modal logic $\textsf{IK}$ using a translation into a suitable (intuitionistic) first-order logic. We axiomatize the logic and give a semantics by means of intuitionistic neighbourhood models, which contain neighbourhoods whose value can change when moving along the intuitionistic accessibility relation. We compare the resulting logic with other intuitionistic monotone modal logics and show how it can be embedded into a multimodal version of $\textsf{IK}$.