I have been approached by a company offering a contract to develop a piece of intelligent software. In the course of pre-contractual negotiations, I'm likely to discuss ideas that may result in new IP. Will I own that IP or will the company own that IP? What rights will I have and what rights will the company have in respect of the ideas and the IP?
Intellectual property rights do not usually protect ideas as such. In particular ideas about the structure, organisation, functionality or design of computer software are generally unprotected by intellectual property law.
Software inventions can be protected by patents, but I will assume that you are not concerned with a patentable invention here. At least in the EU, software patents remain somewhat exceptional.
The principal English law intellectual property protection for software is copyright. Copyright protects specific works, such as computer code, and the first owner of those rights will be the author of the code (or the author's employer).
Accordingly, you will likely own the relevant intellectual property if you go on to write the code, and the company in question will likely go on to own the copyright if its employees go on to write the code, subject to any contract to the contrary. Crucially, and subject to my following comments, as there is no copyright in the "unfixed" ideas themselves, in all likelihood neither you nor the company could block the development or exploitation of code based using the law of copyright by the other.
You should consider, instead, asking the company to sign an non-disclosure agreement before you enter discussions. The non-disclosure agreement should specify that any non-public design/development ideas that you disclose to the company are to be kept secret and not used by the company for any purpose other than the consideration of your proposal. Getting the company to sign the agreement of course is only half the battle - enforcing non-disclosure obligations can be expensive and difficult. Still, an NDA is better than no protection at all.
If you go on to win the contract, the ownership and licensing of the intellectual property rights should be set out in the agreement you sign with the company.
If the ideas themselves are or may be valuable, you should instruct a lawyer to review all the circumstances and advise. Necessarily, I am making a number of assumptions in giving this answer, some of which may be wrong.
Note, also, that the answer is grounded in English law.