Reducing Propositional Theories in Equilibrium Logic to
... equivalent in a strong sense so that theory parts can be translated independent of the wider context in which they might be embedded. It was only recently established [1] that propositional theories are indeed equivalent (in a strong sense) to logic programs. The present paper extends this result wi ...
... equivalent in a strong sense so that theory parts can be translated independent of the wider context in which they might be embedded. It was only recently established [1] that propositional theories are indeed equivalent (in a strong sense) to logic programs. The present paper extends this result wi ...
Adding the Everywhere Operator to Propositional Logic (pdf file)
... with respect to model C, which consists of all states (total functions from the set of all propositional variables to {t, f } , with the conventional definition of evaluation), where every state is accessible from every other state. For example, the formula ¬2p for p a propositional variable is valid ...
... with respect to model C, which consists of all states (total functions from the set of all propositional variables to {t, f } , with the conventional definition of evaluation), where every state is accessible from every other state. For example, the formula ¬2p for p a propositional variable is valid ...
Aristotle`s particularisation
... embraced Aristotle’s particularisation, since he implicitly appealed to Aristotle’s particularisation in his reasoning when needed20 . Now, although we could validly argue that if Aristotle’s particularisation is true, then any first order system that appeals to the standard first order predicate ca ...
... embraced Aristotle’s particularisation, since he implicitly appealed to Aristotle’s particularisation in his reasoning when needed20 . Now, although we could validly argue that if Aristotle’s particularisation is true, then any first order system that appeals to the standard first order predicate ca ...
Propositional Logic: Why? soning Starts with George Boole around 1850
... Propositional logic is not expressive enough to capture that argument ...
... Propositional logic is not expressive enough to capture that argument ...
Introduction to Racket
... Short way to define curried functions. (define ((add x) y) (+ x y)) (define add3 (add 3)) (add3 4) ((add 10) 20) A simple composition of functions (define ((comp f g) . x) (f (apply g x))) (define add2 (comp add1 add1)) (add2 5) ...
... Short way to define curried functions. (define ((add x) y) (+ x y)) (define add3 (add 3)) (add3 4) ((add 10) 20) A simple composition of functions (define ((comp f g) . x) (f (apply g x))) (define add2 (comp add1 add1)) (add2 5) ...
Tools-Slides-3 - Michael Johnson`s Homepage
... Logic is one of the concepts covered in this course. Elementary logic course teachers use logic. ‘Logic’ has 5 letters and means rational. Logic is a subject and so is the name ‘logic.’ ...
... Logic is one of the concepts covered in this course. Elementary logic course teachers use logic. ‘Logic’ has 5 letters and means rational. Logic is a subject and so is the name ‘logic.’ ...
Introduction, Scheme basics (expressions, values)
... To Evaluate a combination: (as opposed to special form) a. Evaluate all of the sub-expressions in some order b. Apply the procedure that is the value of the leftmost sub-expression to the arguments (the values of the other sub-expressions) ...
... To Evaluate a combination: (as opposed to special form) a. Evaluate all of the sub-expressions in some order b. Apply the procedure that is the value of the leftmost sub-expression to the arguments (the values of the other sub-expressions) ...
Introduction to Logic
... Formal Language • Formal logic replaces the ordinary language of argument with a symbolic language. • This language is meant to be free of all ambiguity and vagueness. • The language is meant to wear its logical structure on its face. • Our formal languages: SL and QL. ...
... Formal Language • Formal logic replaces the ordinary language of argument with a symbolic language. • This language is meant to be free of all ambiguity and vagueness. • The language is meant to wear its logical structure on its face. • Our formal languages: SL and QL. ...
1.3.4 Word Grammars
... (M, ), an element m ∈ M is called minimal, if there is no element m0 ∈ M so that m m0 . An element m ∈ M is called smallest, if m0 m for all m0 ∈ M different from m. Note the subtle difference between minimal and smallest. There may be several minimal elements in a set M but only one smallest e ...
... (M, ), an element m ∈ M is called minimal, if there is no element m0 ∈ M so that m m0 . An element m ∈ M is called smallest, if m0 m for all m0 ∈ M different from m. Note the subtle difference between minimal and smallest. There may be several minimal elements in a set M but only one smallest e ...
logica and critical thinking
... There are two ways of evaluating an argument. Formal logic is to use the deductive criterion for evaluating arguments. Informal logic is to use the inductive criterion for evaluating argument. ...
... There are two ways of evaluating an argument. Formal logic is to use the deductive criterion for evaluating arguments. Informal logic is to use the inductive criterion for evaluating argument. ...
Completeness through Flatness in Two
... There are various ways to get around these negative results: for instance in arrow logic, an interesting approach is to drop the constraint that the universe of a model should be a full square. The theory of such relativized squares may be both decidable and nicely axiomatizable (cf. Marx et alii [1 ...
... There are various ways to get around these negative results: for instance in arrow logic, an interesting approach is to drop the constraint that the universe of a model should be a full square. The theory of such relativized squares may be both decidable and nicely axiomatizable (cf. Marx et alii [1 ...
A General Proof Method for ... without the Barcan Formula.*
... accessibility relation in the underlying Kripke semantics. In the original presentation, the Barcan formula, (Vx)La 1 L(Vx)a, and its converse always held, so the domain of individuals was invariant between possible worlds. This is not suitable for all applications because, as we pass from world to ...
... accessibility relation in the underlying Kripke semantics. In the original presentation, the Barcan formula, (Vx)La 1 L(Vx)a, and its converse always held, so the domain of individuals was invariant between possible worlds. This is not suitable for all applications because, as we pass from world to ...
LISP
... the result is stored in memory location which is represented as a variable in the program. A purely functional programming language does not use variables and assignment statements. Without variables iterative constructs are not possible. Repetition must be done by recursion. The execution of a func ...
... the result is stored in memory location which is represented as a variable in the program. A purely functional programming language does not use variables and assignment statements. Without variables iterative constructs are not possible. Repetition must be done by recursion. The execution of a func ...
Completeness Theorem for Continuous Functions and Product
... short, is considered as a minimal subsystem of ZF necessary for a good notion of computation. KP arises from ZF by omitting the Power Set Axiom and restricting Separation and Collection to ∆0 -formulas. An admissible set is a transitive set A such that (A, ∈) is a model of KP. The smallest example o ...
... short, is considered as a minimal subsystem of ZF necessary for a good notion of computation. KP arises from ZF by omitting the Power Set Axiom and restricting Separation and Collection to ∆0 -formulas. An admissible set is a transitive set A such that (A, ∈) is a model of KP. The smallest example o ...
CITS 3242 Programming Paradigms
... So, the current variables can be discarded before the recursive call. Then, the recursive call directly returns a result to the original caller. The compiled code will actually just be a simple loop. This is called tail recursion, and is a very common technique for efficient code. ...
... So, the current variables can be discarded before the recursive call. Then, the recursive call directly returns a result to the original caller. The compiled code will actually just be a simple loop. This is called tail recursion, and is a very common technique for efficient code. ...
Propositional Logic Syntax of Propositional Logic
... Unification in Predicate Logic • The process of finding substitution for variables to make arguments match is called unification. – a substitution is the simultaneous replacement of variable instances by terms, providing a “binding” for the variable – without unification, the matching between rules ...
... Unification in Predicate Logic • The process of finding substitution for variables to make arguments match is called unification. – a substitution is the simultaneous replacement of variable instances by terms, providing a “binding” for the variable – without unification, the matching between rules ...
Part 1
... a set of functional forms to construct complex functions, a function application operation, some structure to represent data In functional programming, functions are viewed as values themselves, which can be computed by other functions and can be parameters to other functions Functions are f ...
... a set of functional forms to construct complex functions, a function application operation, some structure to represent data In functional programming, functions are viewed as values themselves, which can be computed by other functions and can be parameters to other functions Functions are f ...
Functional Programming: Scheme
... Functional Programming and Lambda Calculus • Functional languages have a formal semantics derived from Lambda Calculus: – Defined by Alonzo Church in the mid 1930s as a computational theory of recursive functions. – The lambda calculus emphasizes expressions and functions, which naturally leads ...
... Functional Programming and Lambda Calculus • Functional languages have a formal semantics derived from Lambda Calculus: – Defined by Alonzo Church in the mid 1930s as a computational theory of recursive functions. – The lambda calculus emphasizes expressions and functions, which naturally leads ...
A HIGHER-ORDER FINE-GRAINED LOGIC FOR INTENSIONAL
... models defined for FIL. For reasons of space, we will limit ourselves to an outline of the proof. First it is necessary to prove a lemma stating that if there is a model M , a world w1 , and a valuation g such that for the root 1 s of a finished tree T, kskM,w1 ,g = t, then there is an open path P i ...
... models defined for FIL. For reasons of space, we will limit ourselves to an outline of the proof. First it is necessary to prove a lemma stating that if there is a model M , a world w1 , and a valuation g such that for the root 1 s of a finished tree T, kskM,w1 ,g = t, then there is an open path P i ...
A Tutorial Introduction to the Lambda Calculus
... and a single function definition scheme. It was introduced in the 1930s by Alonzo Church as a way of formalizing the concept of effective computability. The λ calculus is universal in the sense that any computable function can be expressed and evaluated using this formalism. It is thus equivalent to ...
... and a single function definition scheme. It was introduced in the 1930s by Alonzo Church as a way of formalizing the concept of effective computability. The λ calculus is universal in the sense that any computable function can be expressed and evaluated using this formalism. It is thus equivalent to ...
THE HISTORY OF LOGIC
... them, the relevant languages were already fully interpreted, and were not going to be limited to any particular subject-matter. Because the languages are completely general, there is no interesting perspective ‘outside’ the system from which to study it. The orientation of the logicists has been cal ...
... them, the relevant languages were already fully interpreted, and were not going to be limited to any particular subject-matter. Because the languages are completely general, there is no interesting perspective ‘outside’ the system from which to study it. The orientation of the logicists has been cal ...
A Note on Assumptions about Skolem Functions
... An occurrence is a word over IN. Let denote the empty word. Then we define the set of occurrences occ(Φ) of a formula Φ as follows: (i) the empty word is in occ(Φ) (ii) i.π is in occ(Φ) iff Φ = Ψ1 ∧ . . . ∧ Ψn or Φ = Ψ1 ∨ . . . ∨ Ψn , 1 ≤ i ≤ n and π ∈ occ(Ψi ) (iii) 1.π (2.π) is in occ(Φ) iff Φ ...
... An occurrence is a word over IN. Let denote the empty word. Then we define the set of occurrences occ(Φ) of a formula Φ as follows: (i) the empty word is in occ(Φ) (ii) i.π is in occ(Φ) iff Φ = Ψ1 ∧ . . . ∧ Ψn or Φ = Ψ1 ∨ . . . ∨ Ψn , 1 ≤ i ≤ n and π ∈ occ(Ψi ) (iii) 1.π (2.π) is in occ(Φ) iff Φ ...