Tree Languages Defined in First-Order Logic with One Quantifier Alternation

We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the quantifier free part we consider two signatures, either the descendant relation alone or together with the lexicographical order relation on nodes. We provide an effective characterization of tree and forest languages definable in \Delta_2 . This characterization is in terms of algebraic equations. Over words, the class of word languages definable in \Delta_2 forms a robust class, which was given an effective algebraic characterization by Pin and Weil

Piecewise testable tree languages

This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma_1 sentences if and only if its syntactic monoid is J-trivial

Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog

We propose a novel, type-elimination-based method for reasoning in the description logic SHIQbs including DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst case optimal w.r.t. combined and data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for publication in Logical Methods in Computer Scienc

The Wadge Hierarchy of Deterministic Tree Languages

We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner's results on the hierarchy of omega-regular languages of words to the case of trees.Comment: 44 pages, 8 figures; extended abstract presented at ICALP 2006, Venice, Italy; full version appears in LMCS special issu

On logical hierarchies within FO^2-definable languages

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose levels are varieties of languages (and hence admit an algebraic characterization). Using this algebraic approach, we show that the quantifier alternation hierarchy inside FO^{2}[<] is decidable within one unit. For this purpose, we relate each level of the hierarchy with decidable varieties of languages, which can be defined in terms of iterated deterministic and co-deterministic products. A crucial notion in this process is that of condensed rankers, a refinement of the rankers of Weis and Immerman and the turtle languages of Schwentick, Th\'erien and Vollmer.Comment: arXiv admin note: text overlap with arXiv:0904.289

Final Phase I-Phase II Interim Report : Expedited Site Characterization, Morrill, Kansas.

The city of Morrill, Kansas, is located in Brown County, in the northeastern corner of the state. The town lies about 7 mi east of Sabetha and about 10 mi northwest of Hiawatha (Figure 1.1). The population of Morrill as of the 2000 census was approximately 277. The Commodity Credit Corporation (CCC), an agency of the U.S. Department of Agriculture (USDA), operated a grain storage facility in the northwestern section of Morrill from 1950 until 1971. The property continued to be used for grain storage after 1971. Fourteen of the original 21 CCC/USDA circular bin structures remain today. Prior to 1986, commercial grain fumigants containing carbon tetrachloride were commonly used by the CCC/USDA and the grain storage industry to preserve grain. Contamination with carbon tetrachloride, also known as tetrachloromethane, was initially identified in groundwater at Morrill in October 1985 in public water supply well PWS5, during statewide testing of public water supply wells for volatile organic compounds (VOCs). A preliminary assessment was completed by the Kansas Department of Health and Environment (KDHE) in 1989 to obtain background information on the Morrill public water supply and to identify potential sources of the detected carbon tetrachloride contamination (KDHE 1989). Since 1991 the city of Morrill has obtained its water by pipeline from the municipal water supply of Sabetha. Water supplied through the Sabetha system comes from a surface reservoir. Former public wells in Morrill are no longer used for municipal supply. Wells PWS3, PWS4, and PWS5 were plugged in 1993. Wells PWS1 and PWS2 are no longer in active production, but they continue to be available for non-drinking purposes such as bulk hauling for agricultural uses, fire fighting, and road work (Hansen 2001). Because the KDHE found carbon tetrachloride in the groundwater at the former CCC/USDA facility at Morrill that could, in part, be linked to historical use of carbon tetrachloride-based grain fumigants at the facility, the CCC/USDA is conducting an environmental site investigation at Morrill. The investigation at Morrill is being performed by the Environmental Research Division of Argonne National Laboratory. Argonne is a nonprofit, multidisciplinary research center operated by the University of Chicago for the U.S. Department of Energy (DOE). The CCC/USDA has entered into an interagency agreement with DOE, under which Argonne provides technical assistance to the CCC/USDA with environmental site characterization and remediation at its former grain storage facilities. The primary goals of this investigation were (1) to verify any association of carbon tetrachloride with the former CCC/USDA facility; (2) to verify the contaminant migration pathway from the former facility; and (3) to identify any domestic wells located outside the Morrill city limits that are downgradient from and within 1 mi of the former CCC/USDA facility and thus are potential receptors of groundwater contamination