On the complexity of the instance checking problem in concept languages with existential quantification

1993 ◽  
Vol 2 (3) ◽  
pp. 265-278 ◽  
Author(s):  
Andrea Schaerf
Keyword(s):  
Existential Quantification ◽  
Concept Languages

scholarly journals The complexity of existential quantification in concept languages

1992 ◽  
Vol 53 (2-3) ◽  
pp. 309-327 ◽  
Author(s):  
Francesco M. Donini ◽  
Maurizio Lenzerini ◽  
Daniele Nardi ◽  
Bernhard Hollunder ◽  
Werner Nutt ◽  
...  
Keyword(s):  
Existential Quantification ◽  
Concept Languages

scholarly journals On Quantifying Literals in Boolean Logic and its Applications to Explainable AI

2021 ◽  
Vol 72 ◽  
pp. 285-328
Author(s):  
Adnan Darwiche ◽  
Pierre Marquis
Keyword(s):  
Boolean Logic ◽  
Fine Grained ◽  
Explainable Ai ◽  
Boolean Formulas ◽  
Universal Quantification ◽  
Existential Quantification

Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. In this paper, we complement this by introducing and studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification, discuss the interplay between variable/literal and existential/universal quantification, and identify some classes of Boolean formulas and circuits on which quantification can be done efficiently. Literal quantification is more fine-grained than variable quantification as the latter can be defined in terms of the former, leading to a refinement of quantified Boolean logic with literal quantification as its primitive.

scholarly journals Ouk ´Ismen Oudén: Negative Concord and Negative Polarity in the History of Greek

2014 ◽  
Vol 14 (1) ◽  
pp. 43-83 ◽  
Author(s):  
Geoffrey Horrocks
Keyword(s):  
Negative Polarity ◽  
Left Periphery ◽  
Negative Concord ◽  
Ancient Greek ◽  
Polarity Items ◽  
Before And After ◽  
History Of ◽  
Negative Marker ◽  
Existential Quantification ◽  
Single Set

In Ancient Greek a single set of indefinite enclitic pronouns was used indifferently in both negative/affective environments (i.e. like negative polarity items (NPI)) and in positive ones (i.e. like positive polarity items (PPI)). At the same time the negative pronouns used as negative quantifiers (NQ) were also employed as emphatic NPIs, with negative concord. The two functions of each class (i.e. PPI-like vs NPI-like, NQ vs NPI) were determined by syntactic distribution. In the specific case of negative sentences, an indefinite before a sentential negative marker (NM) functioned like a PPI but after a NM like an NPI, while a negative pronoun before a NM was an NQ but after an NM an NPI. This pattern was at odds with the canonical VSO clause structure that evolved in later antiquity, in which focal constituents were contrastively stressed and fronted to the left periphery: neither indefinite nor negative pronouns could be focalised because of the prosodic and/or semantic restrictions on their distribution. This deficiency was eventually remedied by formal/prosodic recharacterisation, the loss of NQs and the generalisation of NPIs to all syntactic positions available to DPs, including the focus position, a process that triggered their reinterpretation as involving universal quantification over negation rather than, as before, existential quantification under negation. The Modern Greek PPI kápjos and NPI kanís are traced from their origins in Ancient Greek and their role in the evolution of the system is explored. The final outcome is typologically to be expected in so far as NQs are redundant in a system in which NPIs appear freely both before and after NMs.

Concept Languages

2021 ◽  
pp. 209-209
Keyword(s):  
Concept Languages

Collective entities and relations in concept languages

1994 ◽  
pp. 13-29
Author(s):  
Jürgen Allgayer ◽  
Enrico Franconi
Keyword(s):  
Concept Languages

Non-first-order features in concept languages

1995 ◽  
pp. 91-102 ◽  
Author(s):  
Francesco M. Donini ◽  
Daniele Nardi ◽  
Riccardo Rosati
Keyword(s):  
First Order ◽  
Concept Languages
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