Related papers: Proving Craig and Lyndon Interpolation Using Label…
We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as…
We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications.
We prove completeness, interpolation, decidability and an omitting types theorem for certain multi dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach…
Given a graph where every node has certain attributes associated with it and some nodes have labels associated with them, Collective Classification (CC) is the task of assigning labels to every unlabeled node using information from the node…
We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Differentiable inductive logic programming (ILP) techniques have proven effective at finding approximate rule-based solutions to link prediction and node classification problems on knowledge graphs; however, the common assumption of…
Inductive logic programming (ILP) has been a deeply influential paradigm in AI, enjoying decades of research on its theory and implementations. As a natural descendent of the fields of logic programming and machine learning, it admits the…
We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…
This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…
We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated…
We present a method for associating labeled directed graphs to finite-dimensional Lie algebras, thereby enabling rapid identification of key structural algebraic features. To formalize this approach, we introduce the concept of…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one…
In this paper we introduce a cut-free sequent calculus for the alternation-free fragment of the modal $\mu$-calculus. This system allows for cyclic proofs and uses a simple focus mechanism to control the unravelling of fixpoints along…
Based on the classical Pl\"ucker correspondence, we present algebraic and geometric properties of discrete integrable line complexes in $CP^3$. Algebraically, these are encoded in a discrete integrable system which appears in various guises…
Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this…