The KE inference system is a tableau method developed by Marco Mondadori which was presented as an improvement, in the computational efficiency sense, over Analytic Tableaux. In the literature, there is no description of a theorem prover based on the KE method for the C"1 paraconsistent logic. Paraconsistent logics have several applications, such as in robot control and medicine. These applications could benefit from the existence of such a prover. We present a sound and complete KE system for C"1, an informal specification of a strategy for the C"1 prover as well as problem families that can be used to evaluate provers for C"1. The C"1KE system and the strategy described in this paper will be used to implement a KE based prover for C"1, which will be useful for those who study and apply paraconsistent logics.
Another tableau system appears in @cite_19 . It was obtained by using a general method for constructing tableau systems @cite_18 . Although this system has a PB branching rule, a feature of systems, is not a system. To be a system it should have only one branching rule, but it has 8 branching rules. Just like the system in @cite_20 , it is based on AT. However, it does not have rules that lead to infinite loops. We do not know of any implementation of this method.
@cite_19 @cite_18 @cite_20
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Given a simple graph G=(V,E) and a set of sources S ⊆ V, denote for each node ν e V by Lν(∞) the lexicographically ordered list of distance source pairs (d(s,v),s), where s ∈ S. For integers d,k ∈ N∪ ∞ , we consider the source detection, or (S,d,k)-detection task, requiring each node v to learn the first k entries of Lν(∞) (if for all of them d(s,v) ≤ d) or all entries (d(s,v),s) ∈ Lν(∞) satisfying that d(s,v) ≤ d (otherwise). Solutions to this problem provide natural generalizations of concurrent breadth-first search (BFS) tree constructions. For example, the special case of k=∞ requires each source s ∈ S to build a complete BFS tree rooted at s, whereas the special case of d=∞ and S=V requires constructing a partial BFS tree comprising at least k nodes from every node in V. In this work, we give a simple, near-optimal solution for the source detection task in the CONGEST model, where messages contain at most O(log n) bits, running in d+k rounds. We demonstrate its utility for various routing problems, exact and approximate diameter computation, and spanner construction. For those problems, we obtain algorithms in the CONGEST model that are faster and in some cases much simpler than previous solutions. Objective A system that translates narrative text in the medical domain into structured representation is in great demand. The system performs three sub-tasks: concept extraction, assertion classification, and relation identification. @PARASPLIT Design The overall system consists of five steps: (1) pre-processing sentences, (2) marking noun phrases (NPs) and adjective phrases (APs), (3) extracting concepts that use a dosage-unit dictionary to dynamically switch two models based on Conditional Random Fields (CRF), (4) classifying assertions based on voting of five classifiers, and (5) identifying relations using normalized sentences with a set of effective discriminating features. @PARASPLIT Measurements Macro-averaged and micro-averaged precision, recall and F-measure were used to evaluate results. @PARASPLIT Results The performance is competitive with the state-of-the-art systems with micro-averaged F-measure of 0.8489 for concept extraction, 0.9392 for assertion classification and 0.7326 for relation identification. @PARASPLIT Conclusions The system exploits an array of common features and achieves state-of-the-art performance. Prudent feature engineering sets the foundation of our systems. In concept extraction, we demonstrated that switching models, one of which is especially designed for telegraphic sentences, improved extraction of the treatment concept significantly. In assertion classification, a set of features derived from a rule-based classifier were proven to be effective for the classes such as conditional and possible. These classes would suffer from data scarcity in conventional machine-learning methods. In relation identification, we use two-staged architecture, the second of which applies pairwise classifiers to possible candidate classes. This architecture significantly improves performance. where (an)n ENo is some sequence of nonnegative numbers, (Sn),nENo is the sequence of partial sums, S0 = 0, Sn = XflXk, of another sequence (Xk)kEN of i.i.d. random variables, and A c R is a fixed Borel set such as [0,1] or [0, oo). Examples of such convolution series are subordinated distributions (f=0Oan = 1) which arise as distributions of random sums, and harmonic and ordinary renewal measures (a0 = 0, an = 1 n for all n C N in the first, an = 1 for all n C NO in the second case). These examples are in turn essential for the analysis of the large time behaviour of diverse applied models such as branching and queueing processes, they are also of interest in connection with representation theorems such as the Levy representation of infinitely divisible distributions. A traditional approach to such problems is via regular variation: If the underlying random variables are nonnegative we can use Laplace transforms and the related Abelian and Tauberian theorems [see, e.g., Stam (1973) in the context of subordination and Feller (1971, XIV.3) in connection with renewal theory; Embrechts, Maejima, and Omey (1984) is a recent treatment of generalized renewal measures along these lines]. The approach of the present paper is based on the Wiener-Levy-Gel'fand theorem and has occasionally been called the Banach algebra method. In Gruibel (1983) we gave a new variant of this method for the special case of lattice distributions, showing that by using the appropriate Banach algebras of sequences, arbitrarily fine expansions are possible under certain assumptions on the higher-order differences of (P(X1 = n))fnEN. Here we give a corresponding treatment of nonlattice distributions. We restrict ourselves to an analogue of first-order differences and obtain a number of theorems which perhaps are described best as next-term results. To explain this let us consider a special case in more detail. The paper presents a one-pass tableau calculus PLTLT for the propositional linear time logic PLTL. The calculus is correct and complete and unlike in previous decision methods, there is no second phase that checks for the fulfillment of the so-called eventuality formulae. This second phase is performed locally and is incorporated into the rules of the calculus. Derivations in PLTLT are cyclic trees rather than cyclic graphs. When used as a basis for a decision procedure, it has the advantage that only one branch needs to be kept in memory at any one time. It may thus be a suitable starting point for the development of a parallel decision method for PLTL.