A Conditional Logical Framework *
... it could be the case that a redex, depending on the result of a communication, can remain stuck until a “good” message arrives from a given channel, firing in that case an appropriate reduction (this is a common situation in many protocols, where “bad” requests are ignored and “good ones” are served ...
... it could be the case that a redex, depending on the result of a communication, can remain stuck until a “good” message arrives from a given channel, firing in that case an appropriate reduction (this is a common situation in many protocols, where “bad” requests are ignored and “good ones” are served ...
Register Allocation
... Opinions differ, and it is difficult to give a precise definition, but generally speaking: • Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; • A functional language is one that supports and encourages the functiona ...
... Opinions differ, and it is difficult to give a precise definition, but generally speaking: • Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; • A functional language is one that supports and encourages the functiona ...
propositional logic extended with a pedagogically useful relevant
... a proof of A, then it is said that A is provable or derivable from any premise set Γ. An obvious example is p ⊢PC q ⊃ q. This is matched by the semantic consequence relation: what holds true in all models is a semantic consequence of every premise set. (ii) Even given (i), further paradoxes derive f ...
... a proof of A, then it is said that A is provable or derivable from any premise set Γ. An obvious example is p ⊢PC q ⊃ q. This is matched by the semantic consequence relation: what holds true in all models is a semantic consequence of every premise set. (ii) Even given (i), further paradoxes derive f ...
Functional Programming
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
Proof Theory of Finite-valued Logics
... domain. Substitutions are denoted by lowercase greek letters and are written as sets of expressions of the form t/x, where t is a (semi-)term and x is a variable. The application of a substitution σ to an expression E is denoted by juxtaposition. Eσ denotes the expression obtained from E by simultan ...
... domain. Substitutions are denoted by lowercase greek letters and are written as sets of expressions of the form t/x, where t is a (semi-)term and x is a variable. The application of a substitution σ to an expression E is denoted by juxtaposition. Eσ denotes the expression obtained from E by simultan ...
Completeness - OSU Department of Mathematics
... Assume x1 , . . . , xn are distinct variables and t1 , . . . , tn are terms. We define the term u(x1 , . . . , xn |t1 , . . . , tn ) by recursion on terms u to be the result of simultaneously replacing each occurence of xi by ti for i = 1, . . . , n (the details definition is straightforward and lef ...
... Assume x1 , . . . , xn are distinct variables and t1 , . . . , tn are terms. We define the term u(x1 , . . . , xn |t1 , . . . , tn ) by recursion on terms u to be the result of simultaneously replacing each occurence of xi by ti for i = 1, . . . , n (the details definition is straightforward and lef ...
Functional
... Useful primitive functions Predicates Arithmetic functions Built-in functions Constructing new functions Temporary variable scopes Control structures: if, case, iteration Output Debugging Comparing functional and imperative languages ...
... Useful primitive functions Predicates Arithmetic functions Built-in functions Constructing new functions Temporary variable scopes Control structures: if, case, iteration Output Debugging Comparing functional and imperative languages ...
Functional Programming
... architecture of the machines on which programs will run Copyright © 2006 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2006 Addison-Wesley. All rights reserved. ...
Expressive Power of SQL
... example, no node has outdegree more than 1)? In this case reachability is in DLOGSPACE, and the argument of [6] does not work. In early 90s, many people were looking into languages for collection types. Functional statically typechecked query languages became quite fashionable, and they were produce ...
... example, no node has outdegree more than 1)? In this case reachability is in DLOGSPACE, and the argument of [6] does not work. In early 90s, many people were looking into languages for collection types. Functional statically typechecked query languages became quite fashionable, and they were produce ...
a. p
... Valid and Invalid Arguments Testing an Argument Form for Validity 1. Identify the premises and conclusion of the argument form. 2. Construct a truth table 3. Look at the row when all the premises are true. If the conclusion is true, it is a valid argument. Otherwise it is invalid ...
... Valid and Invalid Arguments Testing an Argument Form for Validity 1. Identify the premises and conclusion of the argument form. 2. Construct a truth table 3. Look at the row when all the premises are true. If the conclusion is true, it is a valid argument. Otherwise it is invalid ...
On the use of fuzzy stable models for inconsistent classical logic
... implies that we cannot make use of the least model semantics in arbitrary normal residuated logic programs. Example 1. Consider the logic program hp ← ¬q ; 1i interpreted on the residuated lattice with negation ([0, 1], ≤ , min, ←, 1 − x). Then the immediate consequence operator is the mapping: ...
... implies that we cannot make use of the least model semantics in arbitrary normal residuated logic programs. Example 1. Consider the logic program hp ← ¬q ; 1i interpreted on the residuated lattice with negation ([0, 1], ≤ , min, ←, 1 − x). Then the immediate consequence operator is the mapping: ...
Mathematical Logic. An Introduction
... Theorem. Formal theories which are strong enough to “formalize themselves” are not complete, i.e., there are statements such that neither it nor its negation can be proved in that theory. Moreover such theories cannot prove their own consistency. It is no surprise that these results, besides their i ...
... Theorem. Formal theories which are strong enough to “formalize themselves” are not complete, i.e., there are statements such that neither it nor its negation can be proved in that theory. Moreover such theories cannot prove their own consistency. It is no surprise that these results, besides their i ...
Belief Revision in non
... Syntax Let LB be the Belnap language composed of a countable set of propositional letters P B = fp; q; r; : : :g and the connectives :, ^ and _. The set of wffs is obtained by the standard construction mechanism of formulae. For the finite case, a Belnap theory can be seen as a single formula given ...
... Syntax Let LB be the Belnap language composed of a countable set of propositional letters P B = fp; q; r; : : :g and the connectives :, ^ and _. The set of wffs is obtained by the standard construction mechanism of formulae. For the finite case, a Belnap theory can be seen as a single formula given ...
On the computational content of intuitionistic propositional proofs
... in part by NSF grant DMS-9803515. part by a grant A1019901 of the Academy of Sciences of the Czech Republic. 3 Supported in part by a cooperative research grant INT-9600919/ME-103 from the NSF (USA) and the MŠMT (Czech Republic) 2 Supported in ...
... in part by NSF grant DMS-9803515. part by a grant A1019901 of the Academy of Sciences of the Czech Republic. 3 Supported in part by a cooperative research grant INT-9600919/ME-103 from the NSF (USA) and the MŠMT (Czech Republic) 2 Supported in ...
x + 1 - Postech
... Variables are NOT variable. • The contents of a variable never change. • Surprise? – That’s because you are thinking about variables in imperative programming. variables in SML ...
... Variables are NOT variable. • The contents of a variable never change. • Surprise? – That’s because you are thinking about variables in imperative programming. variables in SML ...
D16/B330/3C11 Functional Programming Lecture 5
... Tuple patterns (x,y,z) = (3, “hello”, (34,True,[3])) ...
... Tuple patterns (x,y,z) = (3, “hello”, (34,True,[3])) ...
Bounded Proofs and Step Frames - Università degli Studi di Milano
... The latter is a deduction problem in first-order logic that can be solved affirmatively along the lines indicated in Section 5. The problem can be efficiently discharged by provers like SPASS, E, Vampire.3 In summary, the above is a purely algorithmic procedure, that may or may not succeed (in case ...
... The latter is a deduction problem in first-order logic that can be solved affirmatively along the lines indicated in Section 5. The problem can be efficiently discharged by provers like SPASS, E, Vampire.3 In summary, the above is a purely algorithmic procedure, that may or may not succeed (in case ...
Partial Grounded Fixpoints
... defined several types of fixpoints. They showed that all of the main semantics of logic programming are induced by AFT, using Fitting’s partial immediate consequence operator as an approximator of the two-valued immediate consequence operator. They identified approximating operators for default logi ...
... defined several types of fixpoints. They showed that all of the main semantics of logic programming are induced by AFT, using Fitting’s partial immediate consequence operator as an approximator of the two-valued immediate consequence operator. They identified approximating operators for default logi ...
Functional Programming - TAMU Computer Science Faculty Pages
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
A Mathematical Introduction to Modal Logic
... from a model theoretical point of view. For philosophers, modal logic is a powerful tool for semantics. Many concepts in philosophy of language can be formalized in modal logic. Computer scientists, on the other hand, use modal logic to represent the programs. Model checking and temporal logic are v ...
... from a model theoretical point of view. For philosophers, modal logic is a powerful tool for semantics. Many concepts in philosophy of language can be formalized in modal logic. Computer scientists, on the other hand, use modal logic to represent the programs. Model checking and temporal logic are v ...
Yablo`s paradox
... Stephen Yablo has given an ingenious liar-style paradox that, he claims, avoids self-reference, even of an indirect kind, one that is, in fact, ‘not in any way circular’ (Yablo 1993, his italics). He infers that such circularity is not necessary for this kind of paradox. Some others have agreed.1 Th ...
... Stephen Yablo has given an ingenious liar-style paradox that, he claims, avoids self-reference, even of an indirect kind, one that is, in fact, ‘not in any way circular’ (Yablo 1993, his italics). He infers that such circularity is not necessary for this kind of paradox. Some others have agreed.1 Th ...
Handling Exceptions in nonmonotonic reasoning
... Now, given a knowledge basis comprehending certain and defeasible propositions - we shall call it a defeasible axiomatic basis - what are the inferences supported by this basis? The intuitive normative is “to extract as much information as possible without getting into inconsistency or violating exc ...
... Now, given a knowledge basis comprehending certain and defeasible propositions - we shall call it a defeasible axiomatic basis - what are the inferences supported by this basis? The intuitive normative is “to extract as much information as possible without getting into inconsistency or violating exc ...
Fine`s Theorem on First-Order Complete Modal Logics
... of types [33, 34, 35]. Prior to [14], propositional modal logics were typically taken to be based on a denumerably infinite set of variables, but Fine took the ...
... of types [33, 34, 35]. Prior to [14], propositional modal logics were typically taken to be based on a denumerably infinite set of variables, but Fine took the ...