# applications of logic in computer science

) This page was last edited on 30 May 2020, at 18:09. , There has always been a strong influence from mathematical logic on the field of artificial intelligence (AI). Now in order to query connections with one change of plane we write, q Selection : Selects a subset of tuples from a particular relation, based upon a specified selection cond (i) r {\displaystyle \{d:drinker|\forall b[frequents(d,b)\longrightarrow serves(b,Bud)]\}}, (iv) Find drinkers who frequent only bars serving some beer they like , s Rather than arbitrary formulas with the full range of logical operators the starting point is simply what logicians refer to as modus ponens. y l b r ( | The level of flexibility is ideal for handling the ever changing world of the Internet. ( e ] ) This is the reason why SQL is extended by a counting function. From the beginning of the field it was realized that technology to automate logical inferences could have great potential to solve problems and draw conclusions from facts. s , Consider a companies database that contains all managers together with the 'is superordinate' relation amongst them. f ∃ In this way the model can be validated and any inconsistent definitions flagged. ) u | e ∧ a ) r ( Ron Brachman has described first-order logic (FOL) as the metric by which all AI knowledge representation formalisms should be evaluated. For example, If given a logical system that states "All humans are mortal" and "Socrates is human" a valid conclusion is "Socrates is mortal". | i n ) q However, logic is more suitable for specification of properties (static aspects). " ( This allows specialized theorem provers called classifiers to analyze the various declarations between sets, subsets, and relations in a given model. r , a b e b B : k ( − c e There has always been a strong influence from mathematical logic on the field of artificial intelligence (AI). Relational calculus variant of FO on relational vocabulary (no functions just relations). } ( ∧ ) r However, in specific domains with appropriate formalisms and reusable templates the approach has proven viable for commercial products. ] applications of logic in computer science, neither is it primarily intended to be a first course in logic for students of mathematics or philosophy, although we believe that mush of the material will be increasingly relevant to both of these groups as computational ideas pervade their syllabuses. e i ) ∀ , r k ( It easily becomes clear that FO does not suffice for many cases. e {\displaystyle \cup } So we are fine with FO for a restricted reachibility up to a certain k but not for reachibility as , | ) e ( ∨ r ) n r e = i d Logic for Computer Science/Applications. c ) c ) b s v 1 s ( k {\displaystyle \Pi _{bar}(\Sigma _{beer=Bud}(serves))}, (ii) t , what is not a FO expression. which are not covered in this chaper [chapter | paper]. Temporal logics are being used for modelling systems that flow of time is important. f k Π y − x , In other words, algebra is suitable to say HOW, but logic is suitable to say WHAT. ) ) v  Church first showed the existence of algorithmically unsolvable problems using his notion of lambda-definability. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. q ( ( | i r e The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing. s r , Here, generic application logic is executed on resources throughout the network, including routers and dedicated computing nodes. ( ( u , ∧ u : q Indeed, there is a very amazing one: existential second-order logic corresponds exactly (!) S e Of course this is a trivial example. q Now it is well known that Hamiltonicity is a NP-complete problem and one can ask: is there a natural connection between NP and second order logic? ( In fact it can be shown that reachibility can not be queried in FO. ) Here constants have a fixed interpretation, this is slightly different than in FO logic. d s b {\displaystyle q_{1}(a,b)=\exists _{c}F(a,c)\land F(c,b)} Frame languages such ais KL-ONE have a rigid semantics.

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