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An offence is a term used to describe breaches of the law that constitute a crime.
Offences of basic intent require intention or recklessness, as opposed to offences of specific intent" where only intention will suffice (e.g. murder).
Recklessness is a complex concept, but may loosely be described as the process of deliberately closing one's mind to the obvious risks of a certain action.
Criminal damage is a crime of basic intent. The offence may occur when the defendant caused damage to another's property and the defendant intended it or where the defendant didn't intend it as such, but was reckless as to whether it would occur. For example, an individual throwing a ball against a window may not intend to break the grass, but he/she knows that the glass may break and is proceeding in any event.
Offences of specific intent are offences where it has to be proved that the defendant intended on a specific outcome (or one of several specified outcomes). This contrasts with other offences where the prosecution only need to show that the defendant was reckless.
Examples of offences of specific intent are murder, attempted murder and theft.