Related papers: Nested Sequents for Intuitionistic Multi-Modal Log…
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…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…
Large language models (LLMs) demonstrate strong reasoning abilities in solving complex real-world problems. Yet, the internal mechanisms driving these complex reasoning behaviors remain opaque. Existing interpretability approaches targeting…
In this paper, we discuss Semantic Construction Grammar (SCG), a system developed over the past several years to facilitate translation between natural language and logical representations. Crucially, SCG is designed to support a variety of…
In Linear Logic ($\mathsf{LL}$), the exponential modality $!$ brings forth a distinction between non-linear proofs and linear proofs, where linear means using an argument exactly once. Differential Linear Logic ($\mathsf{DiLL}$) is an…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We prove that the sequent calculus $\mathsf{L_{RBL}}$ for residuated basic logic $\mathsf{RBL}$ has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic $\mathsf{BPL}$. Thus…
We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum.…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…
Verifying real-world programs often requires inferring loop invariants with nonlinear constraints. This is especially true in programs that perform many numerical operations, such as control systems for avionics or industrial plants.…
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented…
We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameter-free admissibility and unification to the setting with…
We introduce an intuitionistic modal logic strictly contained in the intuitionistic modal logic IK and being an appropriate candidate for the title of ``minimal normal intuitionistic modal logic''.
Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic…