a calculus (formal system) that can be interpreted in terms of a particular fragment of deductive logic. Various logical calculi are used as a basis for constructing richer “nonlogical,” for example, mathematical, theories. Examples of logical calculi that can be used for this purpose are ...
In Aristotlean propositions, a predicate is applied to a subject; the Stoics allowed for the recombination of propositions with connectives. Later on, some medieval logicians restricted propositions to particular concrete tokens (in the mind, or spoken, or written). Changing the class of realisers...
Right to left similarly.) Parallel results hold for the other standard connectives ∨, ⊃, ￢, in both Classical and Intuitionistic logic. Parallel results hold for the quantifiers in both logics, though here there is an added subtlety: after all, in Higher Order logics (as in other many...
The deduction of the answer (is a SET/is not a SET) is stated without any previous training. It is an integrable inference in all trials, since premises contain all the predicates used in conclusions (see Introduction) and crucially depends on the definition of SET, hence excluding any non-...
All representations are given in and mechanically verified by the Twelf implementation of LF. Moreover, we use the Twelf module system to treat all connectives and quantifiers independently. Thus, individual connectives are available for reuse when representing other logics, and we obtain the first ...
NLM [96] leverages NNs as function approximators and integrates logic programming to handle objects including properties, relations, logical connectives, and quantifiers. NLM assigns fixed predicates as either True or False on a predetermined set of objects, representing logical predicates using tensors....
holds. Connectives between propositions can be extended to predicates. In particular, if P and Q are predicates with only one argument, then (𝑃→𝑄)(P→Q) denotes the predicate such that (𝑃→𝑄)(𝑎)(P→Q)(a) holds when proposition (...
The connectives, that is, what is usually defined as the symbolic logical operators of implication, conjunction and disjunction, all correspond in LIR to real operators on real elements in the evolution of real dynamic processes. Accordingly, these operators are, also, subject to being actualized,...
In LIR, the connectives, that is, what is usually defined as the symbolic logical operators of implication, conjunction and disjunction, all correspond to real operators on real elements in the evolution of real dynamic processes. Accordingly, these operators are, also, subject to being actualized...