Well, I've run that code through perltidy to see what I can see, and that looks very much like something called spaghetti code ... its to hard to read for humans, to hard to fix for humans, me included

So my advice, if you want to solve your warning, start rewriting the program to work without goto

See Text Based Perl Game and especially the responses (and links in responses) for specifics

So in the end you write something like, something short, where the control-flow is easy to seee (birds eye view), no gotos :) no spaghetti

sub LHCC {
  DECISION:
    while( 1 ) {
        WelcomeMsg();
        my $decision = GetDecision();
        if( $decision =~ /quit/ ) {
            last DECISION;
        } elsif( $decision =~ /ready/ ) {
            GoDoReadyDecision();
        } else {
            TryAgainMessage();
        }
    }
} ## end sub LHCC

sub GoDoReadyDecision {
    my $no_statements = GetNoStatements();
    ...;
    GetQPStatements( \%Statements );
    ...;
    my( $conclusions, $o_conclusions ) =
      ConcludeConclusions( \%Statements, \%Contrapositives ... );

    return $conclusions, $o_conclusions;
} ## end sub GoDoReadyDecision

sub ConcludeConclusions {
    my( $Statements, $Contrapositives ) = @_;
    while( my( $key, $value ) = each %$Statements ) {
        ...;
    }
    for my $key ( keys %$Contrapositives ) {
        my $value = $Contrapositives->{$key};
        ...;
    }
    ...;
    return \@Conclusion, \@OtherConclusion;
} ## end sub ConcludeConclusions
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And when you get "use of unitialized ..." you can focus only on one small subroutine, you Data::Dump::dd( \@_ ) and can debug only this one small part

Good luck