In this paper, we propose a new approach to formalize realworld obligations that may be found in existing legislation. Specifically, we propose to formalize real-world obligations by combining insights of two logical frameworks: Input/Output logic, belonging to the literature in deontic logic and normative reasoning, and the Reification-based approach of Jerry R. Hobbs, belonging to the literat...

We provide a logical matrix semantics and Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. achieve former by introducing closely related to that inducing paracomplete weak Kleene logic, latter presenting where initial sequents left right rules negation are subject linguistic constraints.

This paper presents a language of update programs that integrates logical queries, bulk updates and hypothetical reasoning in a seamless manner. There is no syntactic or semantic distinction between queries and updates. Update programs extend logic programs with negation in both syntax and semantics. Users can specify bulk updates in which an arbitrary update is applied simultaneously for all a...

In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster’s rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitati...

The semantics of a proof language relies on the representation of the state of a proof after a logical rule has been applied. This information, which is usually meaningless from a logical point of view, is fundamental to describe the control mechanism of the proof search provided by the language. In this paper, we propose a datatype, called proof monad, to represent the state information of a p...

The constructor-based logics constitute the logical foundation of the so-called OTS/CafeOBJ method, a modeling, specification and verification method of the observational transition systems. It is well known the important role played in algebraic specifications by the initial algebras semantics. Free models along presentation morphisms provide semantics for the modules with initial denotation i...

Constraint Handling Rules (CHR) is a high-level language commonly used to write constraint solvers. Most CHR programs depend on the refined operational semantics, resulting in an obfuscated logical reading and potential misbehavior under the theoretical operational semantics. We introduce two source to source transformations: guard simplification and occurrence subsumption. By removing redundan...

Usually, semantics of inheritance networks is specified indirectly through a translation into one of the standard logical formalisms. Since such translation involves an algorithmic aspect, which is usually complex, these approaches to inheritance are not truly declarative. We provide a general framework for specifying a direct semantics of inheritance networks. Because the networks are not expr...

Constraint Handling Rules (CHR) is a high-level language commonly used to write constraint solvers. Most CHR programs depend on the refined operational semantics, resulting in an obfuscated logical reading and non-termination or worse under the theoretical operational semantics. We introduce a source to source transformation called guard simplification which allows CHR programmers to write self...

Dung’s argumentation framework takes as input two abstract entities: a set of arguments and a binary relation encoding attacks between these arguments. It returns acceptable sets of arguments, called extensions, wrt a given semantics. While the abstract nature of this setting is seen as a great advantage, it induces a big gap with the application that it is used to. This raises some questions a...