Related papers: Nested Sequents for Quantified Modal Logics
Strict-Tolerant Logic (ST) underpins naive theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
Consequence-based reasoning can be used to construct proofs that explain entailments of description logic (DL) ontologies. In the literature, one can find multiple consequence-based calculi for reasoning in the $\mathcal{EL}$ family of DLs,…
This document serves as a companion to the paper of the same title, wherein we introduce a Gentzen-style sequent calculus for HXPathD. It provides full technical details and proofs from the main paper. As such, it is intended as a reference…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
We present a uniform characterisation of three-valued logics by means of the bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as…
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…
The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
Data-aware modal logics offer a powerful formalism for reasoning about semi-structured queries in languages such as DataGL, XPath, and GQL. In brief, these logics can be viewed as modal systems capable of expressing both reachability…
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space…
We present some hypersequent calculi for all systems of the classical cube and their extensions with axioms $T$, $P$, $D$, and, for every $n\geq 1$, rule $RD^+_n$. The calculi are internal as they only employ the language of the logic, plus…
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…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…