Inference by complementary elimination

1957 ◽  
Vol 22 (3) ◽  
pp. 233-236
Author(s):  
Bernard K. Symonds ◽  
Roderick M. Chisholm
Keyword(s):  
Modus Ponens ◽  
The Other ◽  
Second Step ◽  
Modus Tollens ◽  
Disjunctive Syllogism ◽  
Hypothetical Syllogism

The inferences countenanced by the traditional rules of modus ponens, modus tollens, disjunctive syllogism, hypothetical syllogism, and the complex types of dilemma may be regarded as single applications of one rule of inference, “the rule of complementary elimination”. In the present paper, we shall discuss this rule informally and illustrate it in application to expressions written in the language of Principia Mathematica. Our illustrations will contain no connectives except for those for conjunction, disjunction, and negation; we use parentheses in place of dots; and we allow disjunction and conjunction to have any number of operands more than two.In applying complementary elimination to a set of premises, we take the following three steps, (i) We form, merely by disjoining the premises, an expression which we shall call a premise disjunction, (ii) If we have n premises, we eliminate n minus one (or fewer) pairs of the following sort from our premise disjunction: each pair is such that one of its members is the negation of the other and both members are specific occurrences of disjuncts of our premise disjunction. We shall call such pairs complementary pairs, (iii) The formula obtained by means of our second step is one that may be made well-formed merely by eliminating parentheses or connectives other than negation; we make such elimination, and any formula we thus obtain is a consequence of our premises.

scholarly journals On Basic Probability Logic Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Marija Boričić Joksimović
Keyword(s):  
Probability Theory ◽  
Inference Rule ◽  
Modus Ponens ◽  
Probability Logic ◽  
Modus Tollens ◽  
Short Overview ◽  
Basic Probability ◽  
Probabilistic Version ◽  
Hypothetical Syllogism

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

What participles are a mixture of

Linguistics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Frank Van Eynde
Keyword(s):  
Phrase Structure ◽  
The Other ◽  
Second Step ◽  
Phrase Structure Grammar ◽  
Mixed Nature

Abstract It is commonly assumed that participles show a mixture of verbal and adjectival properties, but the issue of how this mixed nature can best be captured is anything but settled. Analyses range from the purely adjectival to the purely verbal with various shades in between. This lack of consensus is at least partly due to the fact that participles are used in a variety of ways and that an analysis which fits one of them is not necessarily equally plausible for the other. In an effort to overcome the resulting fragmentation this paper proposes an analysis that covers all uses of the participles, from the adnominal over the predicative to the free adjunct uses, including also the nominalized ones. To keep it feasible we focus on one language, namely Dutch. With the help of a treebank we first identify the uses of the Dutch participles and describe their properties in informal terms. In a second step we provide an analysis in terms of the notation of Head-driven Phrase Structure Grammar. A key property of the analysis is the differentiation between core uses and grammaticalized uses. The treatment of the latter is influenced by insights from Grammaticalization Theory.

scholarly journals Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Tao Liao ◽  
Hao-Chih Lee ◽  
Ge Yang ◽  
Yongjie Jessica Zhang
Keyword(s):  
Correspondence Analysis ◽  
Flexible Structures ◽  
Spectral Shape ◽  
The Other ◽  
Shape Deformation ◽  
Second Step ◽  
Analysis Method ◽  
Shape Correspondence ◽  
Dense Point ◽  
Different Shapes

AbstractThe functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the order of modes. An initial correspondence is built based on the distribution of a shape diameter, which matches similar surface features in different shapes and guides the eigenfunction computation. A two-step scheme is developed to determine the final correspondence. The first step utilizes volumetric eigenfunctions to correct the assignment of boundary nodes that disobeys the main structures. The second step minimizes the distortion induced by deforming one shape to the other. As a result, a dense point correspondence is constructed between the two given shapes, based on which we approximate and predict the shape deformation, as well as quantitatively measure the detailed shape differences.

Activities of Trovafloxacin Compared with Those of Other Fluoroquinolones against Purified Topoisomerases and gyrA and grlA Mutants ofStaphylococcus aureus

1999 ◽  
Vol 43 (8) ◽  
pp. 1845-1855 ◽  
Author(s):  
Thomas D. Gootz ◽  
Richard P. Zaniewski ◽  
Suzanne L. Haskell ◽  
Frank S. Kaczmarek ◽  
Alison E. Maurice
Keyword(s):  
Dna Cleavage ◽  
Dna Gyrase ◽  
The Other ◽  
Second Step ◽  
Ofstaphylococcus Aureus ◽  
Topoisomerase Iv ◽  
Direct Plating ◽  
Clinical Strains ◽  
Plating Method ◽  
Susceptibility Breakpoint

ABSTRACT Frequencies of mutation to resistance with trovafloxacin and four other quinolones were determined with quinolone-susceptibleStaphylococcus aureus RN4220 by a direct plating method. First-step mutants were selected less frequently with trovafloxacin (1.1 × 10−10 at 2 to 4× the MIC) than with levofloxacin or ciprofloxacin (3.0 × 10−7 to 3.0 × 10−8 at 2 to 4× the MIC). Mutants with a change in GrlA (Ser80→Phe or Tyr) were most commonly selected with trovafloxacin, ciprofloxacin, levofloxacin, or pefloxacin. First-step mutants were difficult to select with sparfloxacin; however, second-step mutants with mutations in gyrA were easily selected when a preexisting mutation in grlA was present. Against 29 S. aureus clinical isolates with known mutations in gyrA and/or grlA, trovafloxacin was the most active quinolone tested (MIC at which 50% of isolates are inhibited [MIC50] and MIC90, 1 and 4 μg/ml, respectively); in comparison, MIC50s and MIC90s were 32 and 128, 16 and 32, 8 and 32, and 128 and 256 μg/ml for ciprofloxacin, sparfloxacin, levofloxacin, and pefloxacin, respectively. Strains with a mutation in grlA only were generally susceptible to all of the quinolones tested. For mutants with changes in both grlA and gyrA MICs were higher and were generally above the susceptibility breakpoint for ciprofloxacin, sparfloxacin, levofloxacin, and pefloxacin. Addition of reserpine (20 μg/ml) lowered the MICs only of ciprofloxacin fourfold or more for 18 of 29 clinical strains. Topoisomerase IV and DNA gyrase genes were cloned from S. aureus RN4220 and from two mutants with changes in GrlA (Ser80→Phe and Glu84→Lys). The enzymes were overexpressed in Escherichia coli GI724, purified, and used in DNA catalytic and cleavage assays that measured the relative potency of each quinolone. Trovafloxacin was at least five times more potent than ciprofloxacin, sparfloxacin, levofloxacin, or pefloxacin in stimulating topoisomerase IV-mediated DNA cleavage. While all of the quinolones were less potent in cleavage assays with the altered topoisomerase IV, trovafloxacin retained its greater potency relative to those of the other quinolones tested. The greater intrinsic potency of trovafloxacin against the lethal topoisomerase IV target in S. aureus contributes to its improved potency against clinical strains of S. aureus that are resistant to other quinolones.

scholarly journals Accurate processing of human pre-rRNA in vitro.

1989 ◽  
Vol 9 (10) ◽  
pp. 4422-4431 ◽  
Author(s):  
G J Hannon ◽  
P A Maroney ◽  
A Branch ◽  
B J Benenfield ◽  
H D Robertson ◽  
...  
Keyword(s):  
Hela Cell ◽  
18S Rrna ◽  
Cleavage Product ◽  
The Other ◽  
Second Step ◽  
Cleavage Sites ◽  
Initial Cleavage ◽  
External Transcribed Spacer ◽  
Cyclic Phosphate

We report here that the mature 5' terminus of human 18S rRNA is generated in vitro by a two-step processing reaction. In the first step, SP6 transcripts were specifically cleaved in HeLa cell nucleolar extract at three positions near the external transcribed spacer (ETS)-18S boundary. Of these cleavage sites, two were major and the other was minor. RNase T1 fingerprint and secondary nuclease analyses placed the two major cleavage sites 3 and 8 bases upstream from the mature 5' end of 18S rRNA and the minor cleavage site 1 base into the 18S sequence. All three cleavages yielded 5'-hydroxyl, 2'-3'-cyclic phosphate termini and were 5' of adenosine residues in the sequence UACCU, which was repeated three times near the ETS-18S boundary. In the second step, the initial cleavage product containing 3 bases of ETS was converted to an RNA with a 5' terminus identical to that of mature 18S RNA by an activity found in HeLa cell cytoplasmic extracts.

scholarly journals On the generalization of Conway algebra

2018 ◽  
Vol 27 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Seongjeong Kim
Keyword(s):  
Algebraic Structure ◽  
The Other ◽  
Second Step ◽  
Polynomial Invariant ◽  
Binary Operations ◽  
Other Hand ◽  
Skein Relation

In [Przytyski and Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1989) 115–139], Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the Homflypt polynomial invariant. On the other hand, in [Kauffman and Lambropoulou, New invariants of links and their state sum models, arXiv:1703.03655v2 [math.GT] 15 Mar 2017], Kauffman and Lambropoulou introduced new 4-variable invariants of oriented links, which are obtained by two computational steps: in the first step, we apply a skein relation on every mixed crossing to produce unions of unlinked knots. In the second step, we apply another skein relation on crossings of the unions of unlinked knots, which introduces a new variable. In this paper, we will introduce a generalization of the Conway algebra [Formula: see text] with two binary operations and we construct an invariant valued in [Formula: see text] by applying those two binary operations to mixed crossings and pure crossing, respectively. The 4-variable invariant of Kauffman and Lambropoulou with a specific condition is derived from the invariant valued in [Formula: see text]. Moreover, the generalized Conway algebra gives us an invariant of oriented links, which satisfies nonlinear skein relations.

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