Related papers: Tableau methodology for propositional logics
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is…
We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known tree-of-tangles theorems for graphs, matroids and abstract separation systems…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…
We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another…
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to…
This guideline proposes a systematic and operational annotation framework for representing the structure of legal argumentation in judicial decisions. Grounded in theories of legal reasoning and argumentation, the framework aims to reveal…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this…
We consider team semantics for propositional logic, continuing our previous work (Yang & V\"a\"an\"anen 2016). In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an…
There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation…
We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…
We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on…