Sentence examples for exact inferential rules from inspiring English sources
In what follows, the predominant focus will be on the 'philosophy of logic' side of medieval theories of consequence, i.e. how they articulated this very notion, rather than on spelling out the exact inferential rules endorsed by the different authors.
The first idea that definitions are generalized identities motivates the traditional account's inferential rules for definitions.
They have sought to identify some favored property (grammatical particlehood, topic neutrality, permutation invariance, characterizability by inferential rules, etc).
The idea is that logical expressions are those whose meaning, in some sense, is given by "purely inferential" rules.
A necessary property of purely inferential rules is that they regulate only inferential transitions between verbal items, not between extra-verbal assertibility conditions and verbal items, or between verbal items and actions licensed by those items.
But "widow" is not a logical expression, since it's not widely applicable; so one needs to postulate more necessary properties that "purely inferential" rules ought to satisfy.
The basic idea is that the logical constants are distinguished from other sorts of expressions by being "characterizable" in terms of purely inferential rules.
It consists essentially of a number of inferential rules (and/or axioms) that one is happy to accept regardless of the situation in a reasoning process.
ULL essentially contains not only the inferential rules (and/or axioms) of LLL but also supplementary rules (and/or axioms) that can be applied in the absence of abnormality, such as DS.
Central to such a proof-theoretic approach is the formulation of inferential rules governing all the expression-forming operators in question rules that come, preferably, in introduction-elimination pairs.
It is not clear that these additional aspects of use can be captured in "purely inferential" rules, or that they can be derived from aspects of use that can be so captured.
