Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Fragments without Implications of both the Full Lambek Logic and some
  of its Substructural Extensions   In this paper we study some fragments without implications of the (Hilbert)
full Lambek logic $\mathbf{HFL}$ and also some fragments without implications
of some of the substructural extensions of that logic. To do this, we perform
an algebraic analysis of the Gentzen systems defined by the substructural
calculi $\FL_\sigma$. Such systems are extensions of the full Lambek calculus
$\FL$ with the rules codified by a subsequence, $\sigma$, of the sequence $e
w_l w_r c$; where $e$ stands for \emph{exchange}, $w_l$ for \emph{left
weakening}, $w_r$ for \emph{right weakening}, and $c$ for \emph{contraction}.
We prove that these Gentzen systems (in languages without implications) are
algebraizable by obtaining their equivalent algebraic semantics. All these
classes of algebras are varieties of pointed semilatticed monoids and they can
be embedded in their ideal completions. As a consequence of these results, we
reveal that the fragments of the Gentzen systems associated with the calculi
$\FL_\sigma$ are the restrictions of them to the sublanguages considered, and
we also reveal that in these languages, the fragments of the external systems
associated with $\FL[\sigma]$ are the external systems associated with the
restricted Gentzen systems (i.e., those obtained by restriction of
$\FL_\sigma]$ to the implication-less languages considered). We show that all
these external systems without implication have algebraic semantics but they
are not algebraizable (and are not even protoalgebraic). Results concerning
fragments without implication of intuitionistic logic without contraction were
already reported in Bou et al.(2006): On two fragments with negation and
without implication of the logic of residuated lattices. Archive for
Mathematical Logic 45(5) and in Adill\'on et al. (2007): On three
implication-less fragments of t-norm based fuzzy logics. Fuzzy Sets and Systems
158(23).

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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci