We define an invariant of a multi-valued logic gate by considering the number of certain threshold functions associated with the gate. We call this invariant the continuous sensitivity of the gate. We discuss a method for analysing continuous sensitivity of a multi-valued logic gate by using experimental data about the gate. In particular, we will show that this invariant provides a lower bound...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

In explicit state model checking of linear temporal logic properties, a Büchi automaton encodes a temporal property. It interleaves with a Kripke model to form a state space, which is searched for counterexamples. Multi-valued model checking considers additional truth values beyond the Boolean true and false; these values add extra information to the model, e.g. for the purpose of abstraction o...

In model checking, abstractions can cause spurious results, which need to be verified in the concrete system to gain conclusive results. Verification based on multi-valued model checking can distinguish conclusive and inconclusive results, while increasing precision over traditional two-valued overand under-abstractions. This paper describes the theory and implementation of multi-valued model c...

The complexity of todays hardware systems steadily increases. Due to this fact new ways of efficiently describing systems are investigated. A very promising approach in this area is SystemC which is a C++-library. To take advantage of SystemC in the multi-valued domain, the concept of multi-valued logic has to be embedded in SystemC. In this paper such a concept is introduced and details of the...

Counterexamples explain why a desired temporal logic property fails to hold, and as such are considered to be the most useful form of output from model-checkers. Multi-valued model-checking, introduced in [4] is an extension of classical model-checking. Instead of classical logic, it operates on elements of a given De Morgan algebra, e.g. the Kleene algebra [14]. Multi-valued modelchecking has ...

Given a lattice (X,≤,∧,∨) we define a multi-valued operation ∧ which is analogous to a t-norm (i.e. it is commutative, associative, has one as a neutral element and is monotone). The operation is parametrized by the set Q, hence we actually obtain an entire family of such multi-valued t-norms. Similarly we define a family of multi-valued t-conorms ∨ . We show that, when P, Q are chosen appropri...

In this paper we explore how the seminal Dung’s abstract argumentation framework can be extended to handle arguments containing gradual concepts. We allow arguments to have a degree of truth associated with them and we investigate the degree of truth to which each argument can be considered accepted, rejected and undecided by an abstract argumentation semantics. We propose a truth-compositional...

2 General theory 3 2.1 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Some logical calculi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Sequent and tableau calculi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Resolution calculi . . . . . . . . . . . . . . . . . . . . . ...