Logic gate signal

Use MOC3041 solid state relay and it will switch on from TTL signal. If case lamp has low resistance in cold start up condition then use TRIAC along with MOC3041.

You can use a relay as long as it meets or exceeds the resistive load. It would be better to use a Definite Purpose contactor or Lighting contactor.

Bulbs are more than resistive loads. When heated, the resistance increases multiple folds, and that makes initial current very high. After getting heated, bulb is more or less a resistive simple load.

Find out why bulb blows when switched ON or switched OFF. It is often when it is switched ON, it blows. Rarely it blows out when continuously ON.

Not to be rude, but I fully understand how an incandescent light works. But when it is suggested to use a relay, which is fine as long as it can handle the inrush. Most off the shelf general purpose relays can not handle the initial load, thus resulting in welded contacts.

It is just safer to use the DP or Lighting contactors.

Most logic gates can only supply a few milliamps or so, there are exceptions. There are a few relays that can operate on such signal levels, but few and far between I fear.

As already suggested, you need to add a transistor, sometimes two, to amplify the signal to where either a realy can be safely operated of a SSR or even a Triac.

Working with mains needs full training and understanding of the whole concept, I have the impression that you don't have that knowledge.....so remember the Darwin Awards page!!! Best, do not do this until trained somehow.....

As a side issue, since incandescents are about to become extinct, does anybody know whether an SSR can control energy saver lamps without any problems? I'd have tried myself but just haven't got round to it yet.

"Without any problems?" There are no problems, only challenges to overcome. Not only can an SSR be designed to turn on a lamp, an SSR can be poorly designed to turn that lamp on. Also, since other lamps need not be resistive in design they can be designed to confuse SSR designers or ease an SSR designer.

A Triac is normally used and can be driven by a logic gate using sensitive input Triacs.

Or as a Triac Optocouple, directly from most 5 volt logic signals.....