Which logics are supported by z3?

Question

Is there a complete listing of all theories/logics that z3 supports? I have consulted this SMTLIB Tutorial which provides a number of logics, but I do not believe that the list is exhaustive. The z3 documentation itself doesn't seem to specify which logics are supported.

I ask because I have an smt file which cannot be solved under any of the logics in the SMTLIB Tutorial (when specified with 'set-logic'), but can be solved when no logic is specified.

Answer 1

For Z3, I have not seen such a list in the documentation, but you can find it in the source code if you really want to know. The list starts around line 65 of check_logic.cpp. I parsed out the list for you using a scary awk one-liner, and found this as of May 20, 2016 (between Z3 4.4.1 and 4.4.2):

"AUFLIA", "AUFLIRA", "AUFNIRA", "LRA", "QF_ABV", "QF_AUFBV", "QF_UFBV", "QF_AUFLIA", "QF_AX", "QF_BV", "QF_IDL", "QF_RDL", "QF_LIA", "QF_LRA", "QF_NIA", "QF_NRA", "QF_UF", "QF_UFIDL", "QF_UFLIA", "QF_UFLRA", "QF_UFNRA", "UFLRA", "UFNIA", "UFBV", "QF_S"

You can compare this to the official list of SMT-LIB 2 logics.

Probably more importantly for you is what the "best logic" is for your application. It sounds like you have a large and varying set of problems that you want Z3 to apply whatever tactics it can to. In that case, for now, it's best to leave the logic unspecified. The problem is that in SMT-LIB v2.0 there was no all-encompassing logic -- the largest logic by some standards was AUFNIRA, but this does not include, for example, bit vectors. As a result, CVC4 introduced a non-standard ALL_SUPPORTED logic, and Z3 performs best for some classes of problems when no logic is specified. This shortcoming of the SMT-LIB 2.0 standard is addressed in SMT-LIB 2.5, with a new logic called "ALL". However, this is not yet supported by either Z3 or CVC4.

Answer 2

You specify a logic in Z3 to ensure that Z3 uses a particular strategy and engine that is typically useful for the class of formulas expressed in this logic. If no logic is specified, then Z3 falls back to a default mode. There is no logic corresponding to this default mode: it integrates multiple engines.