Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Join-semilattices whose principal filters are pseudocomplemented
  lattices   This paper deals with join-semilattices whose sections, i.e. principal
filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in
the section [b,1] is denoted by a\rightarrow b and can be considered as the
connective implication in a certain kind of intuitionistic logic. Contrary to
the case of Brouwerian semilattices, sections need not be distributive
lattices. This essentially allows possible applications in non-classical
logics. We present a connection of the semilattices mentioned in the beginning
with so-called non-classical implication semilattices which can be converted
into I-algebras having everywhere defined operations. Moreover, we relate our
structures to sectionally and relatively residuated semilattices which means
that our logical structures are closely connected with substructural logics. We
show that I-algebras form a congruence distributive, 3-permutable and weakly
regular variety.

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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph