Systemverilog allows severity control by means of system tasks, also systemverilog allows to enable/disable assertions. Some of the system tasks for this purpose are.

• $assertoff : Stop the checking of all specified assertions until a subsequent $asserton. An assertion that is already executing, including execution of the pass or fail statement, is not affected.
• $assertkill: Abort execution of any currently executing specified assertions and then stop the checking of all specified assertions until a subsequent $asserton.
• $asserton: Reenable the execution of all specified assertions.
• $fatal :Run-time fatal assertion error, which terminates the simulation with an error code. The first argument passed to $fatal shall be consistent with the corresponding argument to the Verilog $finish system task, which sets the level of diagnostic information reported by the tool. Calling $fatal results in an implicit call to $finish.
• $error: Run-time error.
• $warning: Run-time warning, which can be suppressed in a tool-specific manner.
• $info: Indicate that the assertion failure carries no specific severity.

  1 module system_assert();
  2 
  3 reg  clk, grant, request;
  4 time current_time;
  5 
  6 initial begin
  7   clk = 0;
  8   grant   = 0;
  9   request = 0;
 10    #4  request = 1;
 11    #4  grant = 1;
 12    #4  request = 0;
 13    #4  grant = 0;
 14    #4  request = 0;
 15    #4  grant = 1;
 16    #4  request = 0;
 17    #4  $finish;
 18 end
 19 
 20 always  #1  clk = ~clk;
 21 //=================================================
 22 // Assertion used in always block
 23 //=================================================
 24 always @ (posedge clk)
 25 begin
 26   if (grant == 1) begin
 27      CHECK_REQ_WHEN_GNT : assert (grant && request) begin
 28         $info("Seems to be working as expected");
 29      end else begin
 30         current_time = $time;
 31         // We can use all below statements
 32         //    $fatal
 33         //    $error
 34         //    $warning
 35         //    $info
 36          #1  $warning("assert failed at time %0t", current_time);
 37         $assertoff(1,system_assert.CHECK_REQ_WHEN_GNT);
 38      end
 39   end
 40 end
 41 
 42 endmodule

 Info: "system_assert.sv", 27: system_assert.CHECK_REQ_WHEN_GNT: at time 9
 Seems to be working as expected
 Info: "system_assert.sv", 27: system_assert.CHECK_REQ_WHEN_GNT: at time 11
 Seems to be working as expected
 "system_assert.sv", 27: system_assert.CHECK_REQ_WHEN_GNT: started at 13s failed at 13s
         Offending '(grant && request)'
 Warning: "system_assert.sv", 27: system_assert.CHECK_REQ_WHEN_GNT: at time 14
 assert failed at time 13
 Stopping new attempts for assertion CHECK_REQ_WHEN_GNT at time 14s.

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