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function name or connective symbolwhether if we write opx to signify the symbol of the compound operator then predicate name and function name or
unification algorithmhere if notice for instance that to unify two sentences as we must find a substitution that makes the two sentences the same
example of unificationlet now here assume instead that we had these two sentences as knowsjohnx rarr hatesjohn x knowsjack mary thus here
unificationas just above this we have said that the rules of inference for propositional logic detailed in the last lecture can also be required in
implicative normal formthus the sentence is now in cnf in fact for simplification can take place by removing duplicate literals and dropping any
eight-stage process - conjunctive normal formshence we notice the following eight-stage process converts any sentence with cnf as 1 eliminate
conjunctive normal formshowever there for the resolution rule to resolve two sentences so they must both be in a normalised format called as
propositional versions of resolutionjust because of so far weve only looked at propositional versions of resolution however in first-order logic we
binary resolutionhowever we saw unit resolution for a propositional inference rule in the previous lecture a b notb athus we can take
drawbacks to resolution theoremthus the underlining here identifies some drawbacks to resolution theorem proving it only works for true theorems that
resolution methodfor a minor miracle occurred in 1965 where alan robinson published his resolution method as uses a method to generalised version of
proof by contradictionnow for forward chaining and backward chaining both have drawbacks but another approach is to think about proving theorems by
backward chainingin generally given that we are only interested in constructing the path whether we can set our initial state to be the theorem
forward chainingnow we have suppose we have a set of axioms that we know are true statements about the world whether we set these to each be an
chains of inferencenow we have to look at how to get an agent to prove a given theorem using various search strategies thus we have noted in previous
existential introductionnow if we have any sentence as a and variable v that does not occur in a so then for any ground term g such occurs in a than
existential elimination now we have a sentence a is with an existentially quantified variable v so then just for every constant symbol k that it
universal eliminationhere for any sentence there is a containing a universally quantified variable v just for any ground term g so we can substitute
ground substitutionhere the act of performing an instantiation is a function like there is only one possible outcome means we can write it as a
first-order inference ruleshere now we have a clear definition of a first-order model is that we can define soundness for first-order inference rules
propositional truth tablesthere xt is a substitution that replaces all occurances of variable x with a term representing an object t as forallx a
quantifiers and variables - propositional modelthere is one question is arrives that what do sentences containing variables mean in other way of
predicates in propositional modelthe predicates take a number of arguments in which for now we assume are ground terms and represent a relationship
terms in propositional modelthere in first-order logic allows us to talking about properties of objects that the first job for our model delta theta
propositional modelhence a propositional model was simply an assignments of truth values to propositions in distinguish a first-order model is a pair