Related papers: Routley Star in Information-Based Semantics
We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…
This paper presents a thoroughgoing interpretation of a weak relevant logic built over the Dunn-Belnap four-valued semantics in terms of the communication of information in a network of sites of knowledge production (laboratories). The…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
This paper develops a new approach to computational argumentation that is informed by philosophical and linguistic views. Namely, it takes into account two ideas that have received little attention in the literature on computational…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
Multi-relational networks are used extensively to structure knowledge. Perhaps the most popular instance, due to the widespread adoption of the Semantic Web, is the Resource Description Framework (RDF). One of the primary purposes of a…
This article contributes in that it clarifies and indeed completes an approach (initiated by Dunn and this author several years ago and again pursued by the present author over the last three years or so) to the relational semantics of…
A Conway semiring is a semiring $S$ equipped with a unary operation $^*:S \to S$, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally…
Separation logic adds two connectives to assertion languages: separating conjunction * ("star") and its adjoint, separating implication -* ("magic wand"). Comparatively, separating implication is less widely used. This paper demonstrates…
We present a first result towards the use of entailment in- side relational dual tableau-based decision procedures. To this end, we introduce a fragment of RL(1) which admits a restricted form of composition, (R ; S) or (R ; 1), where the…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for…
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…
Recent studies have drawn attention to the untapped potential of the "star operation" (element-wise multiplication) in network design. While intuitive explanations abound, the foundational rationale behind its application remains largely…
The interpretability logic of a mathematical theory describes the structural behavior of interpretations over that theory. Different theories have different logics. This paper from 2011 revolves around the question what logic describes the…