Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A modal logic amalgam of classical and intuitionistic propositional
  logic   A famous result, conjectured by G\"odel in 1932 and proved by McKinsey and
Tarski in 1948, says that $\varphi$ is a theorem of intuitionistic
propositional logic IPC iff its G\"odel-translation $\varphi'$ is a theorem of
modal logic S4. In this paper, we extend an intuitionistic version of modal
logic S1+SP, introduced in our previous paper (S. Lewitzka, Algebraic semantics
for a modal logic close to S1, J. Logic and Comp., doi:10.1093/logcom/exu067)
to a classical modal logic L and prove the following: a propositional formula
$\varphi$ is a theorem of IPC iff $\square\varphi$ is a theorem of L (actually,
we show: $\Phi\vdash_{IPC}\varphi$ iff $\square\Phi\vdash_L\square\varphi$, for
propositional $\Phi,\varphi$). Thus, the map $\varphi\mapsto\square\varphi$ is
an embedding of IPC into L, i.e. L contains a copy of IPC. Moreover, L is a
conservative extension of classical propositional logic CPC. In this sense, L
is an amalgam of CPC and IPC. We show that L is sound and complete w.r.t. a
class of special Heyting algebras with a (non-normal) modal operator.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg