Sense and denotation as algorithm and value
... a faithful translation of (11) is that they both express the same algorithm for determining their truth: check to see if at any time Niarchos and Onassis were married to two sisters. On this account, we can define a faithful translation (at the sentence level) as an arbitrary syntactic transformatio ...
... a faithful translation of (11) is that they both express the same algorithm for determining their truth: check to see if at any time Niarchos and Onassis were married to two sisters. On this account, we can define a faithful translation (at the sentence level) as an arbitrary syntactic transformatio ...
Probabilistic Modelling, Inference and Learning using Logical
... whose intended meaning is a function that takes a number x and returns x + x. To apply that function to the constant 42, for example, we use application to form the term (λx.((+ x) x) 42). ...
... whose intended meaning is a function that takes a number x and returns x + x. To apply that function to the constant 42, for example, we use application to form the term (λx.((+ x) x) 42). ...
PDF
... Based on all this, non-trivial reasoning about the behaviour of protocols can be carried out assertionally. Many protocols have been proved correct using BAN logic, and aws in many protocols have been detected using it as well. But this approach – the idealisation process, in particular – has met wi ...
... Based on all this, non-trivial reasoning about the behaviour of protocols can be carried out assertionally. Many protocols have been proved correct using BAN logic, and aws in many protocols have been detected using it as well. But this approach – the idealisation process, in particular – has met wi ...
Knowledge Representation and Reasoning
... property of entities. For instance, we may know that ‘every dog is a mammal’. Such facts are represented in predicate logic by means of universal quantification. ...
... property of entities. For instance, we may know that ‘every dog is a mammal’. Such facts are represented in predicate logic by means of universal quantification. ...
A constructive approach to nonstandard analysis*
... us here. As for Brouwer intuitionism [B] there is a first attempt by Vesley [31]. Moerdijk and Reyes [20] use topos theory to develop calculus with different kinds of infinitesimals. The logic used in the formal theories of their approach is intuitionistic, but the necessary properties of their mode ...
... us here. As for Brouwer intuitionism [B] there is a first attempt by Vesley [31]. Moerdijk and Reyes [20] use topos theory to develop calculus with different kinds of infinitesimals. The logic used in the formal theories of their approach is intuitionistic, but the necessary properties of their mode ...
recursive functions
... A formal system designed to investigate function definition function application recursion Can be called the smallest universal programming language. It is universal in the sense that any computable function can be expressed within this formalism. Thus, it is equivalent in expressive power to Turing ...
... A formal system designed to investigate function definition function application recursion Can be called the smallest universal programming language. It is universal in the sense that any computable function can be expressed within this formalism. Thus, it is equivalent in expressive power to Turing ...
(pdf)
... is a nonempty set, β is a variable assignment function and I is an interpretation function with domain the set of all constants, relations and function symbols in L such that: (1) For every constant symbol c ∈ L, we have that I(c) ∈ A. (2) For every function symbol f ∈ L with arity n, we have that I ...
... is a nonempty set, β is a variable assignment function and I is an interpretation function with domain the set of all constants, relations and function symbols in L such that: (1) For every constant symbol c ∈ L, we have that I(c) ∈ A. (2) For every function symbol f ∈ L with arity n, we have that I ...
Functional Programming
... function/operator name & arguments are evaluated in unspecified order note: if argument is a functional expression, evaluate recursively the resulting function is applied to the resulting values (car '(a b c)) ...
... function/operator name & arguments are evaluated in unspecified order note: if argument is a functional expression, evaluate recursively the resulting function is applied to the resulting values (car '(a b c)) ...
Modular Sequent Systems for Modal Logic
... permute down below the rules cut, 2 and ∧, so we generalise these rules as in Figure 3. We define a contraction-free system K− as K− = K − ctr + {med, m2, m∧} and will show cut elimination for that system, but first we develop the machinery to show that cut elimination for K− leads to cut-eliminatio ...
... permute down below the rules cut, 2 and ∧, so we generalise these rules as in Figure 3. We define a contraction-free system K− as K− = K − ctr + {med, m2, m∧} and will show cut elimination for that system, but first we develop the machinery to show that cut elimination for K− leads to cut-eliminatio ...
CSC 533: Programming Languages Spring 2017
... LISP LISP is very simple and orthogonal § only 2 kinds of data objects 1. atoms (identifiers, strings, numbers, …) 2. lists (of atoms and sublists) unlike arrays, lists do not have to store items of same type/size do not have to be stored contiguously do not have to provide random access § all ...
... LISP LISP is very simple and orthogonal § only 2 kinds of data objects 1. atoms (identifiers, strings, numbers, …) 2. lists (of atoms and sublists) unlike arrays, lists do not have to store items of same type/size do not have to be stored contiguously do not have to provide random access § all ...
A Prologue to the Theory of Deduction
... do not only play the leading role in language, but everything is reduced to them. This applies not only to classically minded theories where the essential, and desirable, quality of propositions is taken to be truth, but also to other theories, like constructivism in mathematics, or verificationism i ...
... do not only play the leading role in language, but everything is reduced to them. This applies not only to classically minded theories where the essential, and desirable, quality of propositions is taken to be truth, but also to other theories, like constructivism in mathematics, or verificationism i ...
Concept Hierarchies from a Logical Point of View
... set Σ as atomic propositions (or propositional variables). Then B∞ [Σ] is the class of all (possibly infinitary) propositional formulas over Σ. A (propositional) theory over Σ is a set of formulas over Σ. Let 2 be a set {0, 1} of two elements equipped with the standard Boolean operations. A 2-valued ...
... set Σ as atomic propositions (or propositional variables). Then B∞ [Σ] is the class of all (possibly infinitary) propositional formulas over Σ. A (propositional) theory over Σ is a set of formulas over Σ. Let 2 be a set {0, 1} of two elements equipped with the standard Boolean operations. A 2-valued ...
Isabelle/HOL for Reachability Analysis of Continuous Systems
... of higher derivatives of the ODE. An approach that would (from a verification point of view) better scale to higher orders would be Taylor series based methods with automatic differentiation (like in VNODE [10]). Setting up concrete instances of our tool still requires a lot of manual interaction, w ...
... of higher derivatives of the ODE. An approach that would (from a verification point of view) better scale to higher orders would be Taylor series based methods with automatic differentiation (like in VNODE [10]). Setting up concrete instances of our tool still requires a lot of manual interaction, w ...
Topological Completeness of First-Order Modal Logic
... a completeness proof for first-order S4 modal logic with respect to topologicalsheaf semantics of Awodey-Kishida [3], which combines the possible-world formulation of sheaf semantics with the topos-theoretic interpretation of the 2 operator and of other symbols. Hence the logic we consider has the f ...
... a completeness proof for first-order S4 modal logic with respect to topologicalsheaf semantics of Awodey-Kishida [3], which combines the possible-world formulation of sheaf semantics with the topos-theoretic interpretation of the 2 operator and of other symbols. Hence the logic we consider has the f ...
vmcai - of Philipp Ruemmer
... branch, the close-ll rule yields the interpolant false, which is carried through by not-left. The rule or-left-l takes the interpolants of its two subproofs and generates false ∨ p(d). This is the final interpolant, since the last rule andleft propagates interpolants without applying modifications. ...
... branch, the close-ll rule yields the interpolant false, which is carried through by not-left. The rule or-left-l takes the interpolants of its two subproofs and generates false ∨ p(d). This is the final interpolant, since the last rule andleft propagates interpolants without applying modifications. ...
Functionalprogramming
... This uniformity of data and programs gives functional programming languages their flexibility and expressive power: programs can be manipulated as data. A one-page interpreter of Lisp in Lisp was the basis of a first ever bootstrapping implementation of a programming language (a very powerful ...
... This uniformity of data and programs gives functional programming languages their flexibility and expressive power: programs can be manipulated as data. A one-page interpreter of Lisp in Lisp was the basis of a first ever bootstrapping implementation of a programming language (a very powerful ...
PPT
... procedure p(a : array [1..10] of integer) procedure p(n: integer, a : array [1..n] of integer) • Attempt at orthogonal design backfires – parameter must be given a type – type cannot contain variables How could this have happened? Emphasis on teaching ...
... procedure p(a : array [1..10] of integer) procedure p(n: integer, a : array [1..n] of integer) • Attempt at orthogonal design backfires – parameter must be given a type – type cannot contain variables How could this have happened? Emphasis on teaching ...
Example
... – Substitute the actual for the formal in the function body. – Evaluate the body. – Return its value as the answer. • Sometimes outermost evaluation does redundant work because it re-evaluates an actual parameter. A clever implementation would have kept track of the substituted copies and recognize ...
... – Substitute the actual for the formal in the function body. – Evaluate the body. – Return its value as the answer. • Sometimes outermost evaluation does redundant work because it re-evaluates an actual parameter. A clever implementation would have kept track of the substituted copies and recognize ...
Sequent-Systems for Modal Logic
... brief discussion of some views on the notion of a logical constant and on alternative logics to which our results might be leading. Most of our demonstrations will be given in a rather sketchy form, or will be omitted altogether, but we suppose that none of them is so difficult that it could not be ...
... brief discussion of some views on the notion of a logical constant and on alternative logics to which our results might be leading. Most of our demonstrations will be given in a rather sketchy form, or will be omitted altogether, but we suppose that none of them is so difficult that it could not be ...
A Concise Introduction to Mathematical Logic
... on certain aims of the formalization. Basic metatheoretic tools are in any case the naive natural numbers and inductive proof procedures. We will sometimes call them proofs by metainduction, in particular when talking about formalized object theories that speak about natural numbers. Induction can l ...
... on certain aims of the formalization. Basic metatheoretic tools are in any case the naive natural numbers and inductive proof procedures. We will sometimes call them proofs by metainduction, in particular when talking about formalized object theories that speak about natural numbers. Induction can l ...
