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While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…
Humans commonly solve complex problems by decomposing them into easier subproblems and then combining the subproblem solutions. This type of compositional reasoning permits reuse of the subproblem solutions when tackling future tasks that…
We prove, and mechanize in Rocq, an abstract obstruction theorem for primitive closure predicates, defined as $C : \mathsf{Form} \to \mathsf{Prop}$ over the closed implication-falsity fragment $A,B ::= \bot \mid A \to B$. Two structurally…
A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of…
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
We study stochastic choice across decision problems, each represented as a menu of action labels paired with observable outcome vectors. We propose a consistency condition for behavior in decision problems composed of two separable…
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent.…
Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow…
We have previously introduced role logic as a notation for describing properties of relational structures in shape analysis, databases and knowledge bases. A natural fragment of role logic corresponds to two-variable logic with counting and…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
Most automated verifiers for separation logic target the symbolic-heap fragment, disallowing both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the…
We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
In knowledge graph construction, a challenging issue is how to extract complex (e.g., overlapping) entities and relationships from a small amount of unstructured historical data. The traditional pipeline methods are to divide the extraction…
This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by…
We propose a hybrid architecture that integrates decision tree-based symbolic reasoning with the generative capabilities of large language models (LLMs) within a coordinated multi-agent framework. Unlike prior approaches that loosely couple…