Related papers: Grading Adjoint Logic
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
This paper explores goal-directed proof search in first-order multi-modal logic. The key issue is to design a proof system that respects the modularity and locality of assumptions of many modal logics. By forcing ambiguities to be…
Using feature-based Tree Adjoining Grammar (TAG), this paper presents linguistically motivated analyses of constructions claimed to require multi-component adjunction. These feature-based TAG analyses permit parsing of these constructions…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
We propose a novel ranking-based semantics for Dung-style argumentation frameworks with the help of conditional logics. Using an intuitive translation for an argumentation framework to generate conditionals, we can apply nonmonotonic…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…