A Paraconsistent Higher Order Logic

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker, Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte

Automating Access Control Logics in Simple Type Theory with LEO-II

Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory (which is also known as higher-order logic) and we have demonstrated that the higher-order theorem prover LEO-II can automate reasoning in and about them. In this paper we combine these results and describe a sound and complete embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEO-II can be applied to automate reasoning in prominent access control logics.Comment: ii + 20 page

Diverse novel mesorhizobia nodulate New Zealand native Sophora species

Forty eight rhizobial isolates from New Zealand (NZ) native Sophora spp. growing in natural ecosystems were characterised. Thirty eight isolates across five groups showed greatest similarity to Mesorhizobium ciceri LMG 14989T with respect to their 16S rRNA and concatenated recA, glnll and rpoB sequences. Seven isolates had a 16S rRNA sequence identical to M. amorphae ATCC 19665T but showed greatest similarity to M. septentrionale LMG 23930T on their concatenated recA, glnll and rpoB sequences. All isolates grouped closely together for their nifH, nodA and nodC sequences, clearly separate from all other rhizobia in the GenBank database. None of the type strains closest to the Sophora isolates based on 16S rRNA sequence similarity nodulated Sophora microphylla but they all nodulated their original host. Twenty one Sophora isolates selected from the different 16S rRNA groupings produced N2-fixing nodules on three Sophora spp. but none nodulated any host of the type strains for the related species. DNA hybridisations indicated that these isolates belong to novel Mesorhizobium spp. that nodulate NZ native Sophora species

Mesorhizobium waimense sp. nov. isolated from Sophora longicarinata root nodules and Mesorhizobium cantuariense sp. nov. isolated from Sophora microphylla root nodules

In total 14 strains of Gram-stain-negative, rod-shaped bacteria were isolated from Sophora longicarinata and Sophora microphylla root nodules and authenticated as rhizobia on these hosts. Based on the 16S rRNA gene phylogeny, they were shown to belong to the genus Mesorhizobium, and the strains from S. longicarinata were most closely related to Mesorhizobium amorphae ACCC 19665(T) (99.8-99.9 %), Mesorhizobium huakuii IAM 14158(T) (99.8-99.9 %), Mesorhizobium loti USDA 3471(T) (99.5-99.9 %) and Mesorhizobium septentrionale SDW 014(T) (99.6-99.8 %), whilst the strains from S. microphylla were most closely related to Mesorhizobium ciceri UPM-Ca7(T) (99.8-99.9 %), Mesorhizobium qingshengii CCBAU 33460(T) (99.7 %) and Mesorhizobium shangrilense CCBAU 65327(T) (99.6 %). Additionally, these strains formed two distinct groups in phylogenetic trees of the housekeeping genes glnll, recA and rpoB. Chemotaxonomic data, including fatty acid profiles, supported the assignment of the strains to the genus Mesorhizobium and allowed differentiation from the closest neighbours. Results of DNA-DNA hybridizations, MALDI- TOF MS analysis, ERIC-PCR, and physiological and biochemical tests allowed genotypic and phenotypic differentiation of our strains from their closest neighbouring species. Therefore, the strains isolated from S. longicarinata and S. microphylla represent two novel species for which the names Mesorhizobium waimense sp. nov. (ICMP 19557(T)=LMG 28228(T)=HAMBI 3608(T)) and Mesorhizobium cantuariense sp. nov. (ICMP 19515(T)=LMG 28225(T)=HAMBI 3604(T)), are proposed respectively

A proposal for broad spectrum proof certificates

International audienceRecent developments in the theory of focused proof systems provide flexible means for structuring proofs within the sequent calculus. This structuring is organized around the construction of ''macro'' level inference rules based on the ''micro'' inference rules which introduce single logical connectives. After presenting focused proof systems for first-order classical logics (one with and one without fixed points and equality) we illustrate several examples of proof certificates formats that are derived naturally from the structure of such focused proof systems. In principle, a proof certificate contains two parts: the first part describes how macro rules are defined in terms of micro rules and the second part describes a particular proof object using the macro rules. The first part, which is based on the vocabulary of focused proof systems, describes a collection of macro rules that can be used to directly present the structure of proof evidence captured by a particular class of computational logic systems. While such proof certificates can capture a wide variety of proof structures, a proof checker can remain simple since it must only understand the micro-rules and the discipline of focusing. Since proofs and proof certificates are often likely to be large, there must be some flexibility in allowing proof certificates to elide subproofs: as a result, proof checkers will necessarily be required to perform (bounded) proof search in order to reconstruct missing subproofs. Thus, proof checkers will need to do unification and restricted backtracking search

System Description: The Proof Transformation System CERES

The original publication is available at www.springerlink.comInternational audienceCut-elimination is the most prominent form of proof trans- formation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolu- tion) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of an ACNF, an LK-proof with only atomic cuts. The system CERES, an implementation of the CERES-method has been used successfully in analyzing nontrivial mathematical proofs (see [4]).In this paper we describe the main features of the CERES system with spe- cial emphasis on the extraction of Herbrand sequents and simplification methods on these sequents. We demonstrate the Herbrand sequent ex- traction and simplification by a mathematical example

Naming Proofs in Classical Propositional Logic

Rapport interne.We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a "real'' sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures, and we get "Boolean'' categories which are not posets