lecture notes in Mathematical Logic
... routine, and to decide provability is in general not even possible. It became a question, then, what exactly should we consider a mechanical procedure; which integer functions, for instance, can we consider to be effectively computable, i.e. such that the computation of their function values can be ...
... routine, and to decide provability is in general not even possible. It became a question, then, what exactly should we consider a mechanical procedure; which integer functions, for instance, can we consider to be effectively computable, i.e. such that the computation of their function values can be ...
On the Complexity of Linking Deductive and Abstract Argument
... equivalent to the negation of the conclusion of the other) and undercut (where the conclusion of the attacker contradicts some part of the support of the other). It is not hard to see that the rebuttal relation between arguments will be symmetric, and this potentially limits its value as an analytic ...
... equivalent to the negation of the conclusion of the other) and undercut (where the conclusion of the attacker contradicts some part of the support of the other). It is not hard to see that the rebuttal relation between arguments will be symmetric, and this potentially limits its value as an analytic ...
34-2.pdf
... and problems that admit good local search solutions, and more discussion of the connection with matroids and greedy algorithms. There is perhaps too much focus on the slightly pathological TSP-nonlocality proof – this proof could have been condensed or simply referenced. 4) Approximation Algorithms ...
... and problems that admit good local search solutions, and more discussion of the connection with matroids and greedy algorithms. There is perhaps too much focus on the slightly pathological TSP-nonlocality proof – this proof could have been condensed or simply referenced. 4) Approximation Algorithms ...
Dynamic logic of propositional assignments
... use bounded iteration “π≤n ”, i.e., iteration up to integer n, as S a macro for k≤n πk . A program is said to be sequential if it is built up from atomic programs and tests by means of the operator “;”. We abbreviate the logical connectives ∧, → and ↔ in the usual way. Aside the dynamic operator hπi ...
... use bounded iteration “π≤n ”, i.e., iteration up to integer n, as S a macro for k≤n πk . A program is said to be sequential if it is built up from atomic programs and tests by means of the operator “;”. We abbreviate the logical connectives ∧, → and ↔ in the usual way. Aside the dynamic operator hπi ...
Quantifiers
... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...
... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...
Cylindric Modal Logic - Homepages of UvA/FNWI staff
... interesting bridge over the gap between propositional formalisms and first-order logic. And second, the modal tools developed in studying cylindric modal logic will be applied to analyze some problems in algebraic logic. To start with the first point, let us consider (multi-)modal logic; here corres ...
... interesting bridge over the gap between propositional formalisms and first-order logic. And second, the modal tools developed in studying cylindric modal logic will be applied to analyze some problems in algebraic logic. To start with the first point, let us consider (multi-)modal logic; here corres ...
Supervaluationism and Classical Logic
... somewhat surprising claim that there’s actually such an n (they claim we know the existential generalization ‘there is an n that such and such’ even if there is no particular n of which we know that such and such). Many philosophers, however, find this claim something too hard to swallow and take it ...
... somewhat surprising claim that there’s actually such an n (they claim we know the existential generalization ‘there is an n that such and such’ even if there is no particular n of which we know that such and such). Many philosophers, however, find this claim something too hard to swallow and take it ...
Bibliography - UCL Computer Science
... Eisenbach S. (ed.) Functional Programming, languages, tools and architectures A collection of introductory articles covering other Functional programming languages (HOPE and FP), practice, theory and implementation. Chapter 4 is of particular interest in that it shows that the functional style of pr ...
... Eisenbach S. (ed.) Functional Programming, languages, tools and architectures A collection of introductory articles covering other Functional programming languages (HOPE and FP), practice, theory and implementation. Chapter 4 is of particular interest in that it shows that the functional style of pr ...
a Decidable Language Supporting Syntactic Query Difference
... complexity of deciding containment over CQ and CQ is Π2P . Containment between Datalog programs (Support recursion, but not negation) is undecidable[18]. Containment of a Datalog program within a conjunctive query is doubly exponential[8], while the converse question is easier. Though there has be ...
... complexity of deciding containment over CQ and CQ is Π2P . Containment between Datalog programs (Support recursion, but not negation) is undecidable[18]. Containment of a Datalog program within a conjunctive query is doubly exponential[8], while the converse question is easier. Though there has be ...
Elements of Functional Programming
... first of the arguments to the original function, and returns a new function which takes the remainder of the arguments and returns the result, is called currying. The technique is named after logician Haskell Curry, though it was invented by other scientists before. Thanks to currying, multiple-argum ...
... first of the arguments to the original function, and returns a new function which takes the remainder of the arguments and returns the result, is called currying. The technique is named after logician Haskell Curry, though it was invented by other scientists before. Thanks to currying, multiple-argum ...
Chapter 6: The Deductive Characterization of Logic
... reflexivity rule for identity (given “nothing”, one is entitled to write down ‘τ = τ’ for any singular term). The existence of zero-place rules is critical if we are to have a non-trivial notion of proof, as defined in the previous section. In particular, a proof must have a first line; since such a ...
... reflexivity rule for identity (given “nothing”, one is entitled to write down ‘τ = τ’ for any singular term). The existence of zero-place rules is critical if we are to have a non-trivial notion of proof, as defined in the previous section. In particular, a proof must have a first line; since such a ...
Action Logic and Pure Induction
... no finite list of equations of REG from which the rest of REG may be inferred. But in addition to this syntactic problem, REG has a semantic problem. It is not strong enough to constrain a∗ to be the reflexive transitive closure of a. We shall call a reflexive when 1 ≤ a and transitive when aa ≤ a, ...
... no finite list of equations of REG from which the rest of REG may be inferred. But in addition to this syntactic problem, REG has a semantic problem. It is not strong enough to constrain a∗ to be the reflexive transitive closure of a. We shall call a reflexive when 1 ≤ a and transitive when aa ≤ a, ...
Separation Logic with One Quantified Variable
... separation logic are PSPACE-complete problems [6]. Decidable fragments with first-order quantifiers can be found in [11, 4]. However, these known results crucially rely on the memory model addressing cells with two record fields (undecidability of 2SL in [6] is by reduction to the first-order theor ...
... separation logic are PSPACE-complete problems [6]. Decidable fragments with first-order quantifiers can be found in [11, 4]. However, these known results crucially rely on the memory model addressing cells with two record fields (undecidability of 2SL in [6] is by reduction to the first-order theor ...
Diagrammatic Reasoning in Separation Logic
... proof sch-pf would be a function of the length of the list, such that sch-pf (n) is a proof that lists specifically of length n are reversed by the program. A disadvantage of this approach is that it requires at least one example proof from the user in every case. Possible future work would be to lo ...
... proof sch-pf would be a function of the length of the list, such that sch-pf (n) is a proof that lists specifically of length n are reversed by the program. A disadvantage of this approach is that it requires at least one example proof from the user in every case. Possible future work would be to lo ...
Beginning with the Haskell Programming Language About the Tutorial
... second part, often (but not always) some ad hoc variables are provided to the left of the equal sign that are involved in the computation to the right. Unlike variables in C, however--and much like variables in mathematics--the Haskell variables refer to the exact same "unknown quantity" on both sid ...
... second part, often (but not always) some ad hoc variables are provided to the left of the equal sign that are involved in the computation to the right. Unlike variables in C, however--and much like variables in mathematics--the Haskell variables refer to the exact same "unknown quantity" on both sid ...
Programming Language Theory and its Implementation
... the books by Gries 26] and Backhouse 3]. The -calculus is a theory of higher-order functions, i.e. functions that take functions as arguments or return functions as results. It has inspired the design of functional programming languages including LISP 53], ML 55], Miranda 70] and Ponder 17]. T ...
... the books by Gries 26] and Backhouse 3]. The -calculus is a theory of higher-order functions, i.e. functions that take functions as arguments or return functions as results. It has inspired the design of functional programming languages including LISP 53], ML 55], Miranda 70] and Ponder 17]. T ...
First-Order Logic, Second-Order Logic, and Completeness
... semantics”. (What are the criteria for the “right” semantics? On which independent, i.e. non-question-begging grounds can we decide? Is the “right” semantics “right” tout court or is it the “right” one with respect to some purpose? Is there only one “right” semantics?) A more direct approach is call ...
... semantics”. (What are the criteria for the “right” semantics? On which independent, i.e. non-question-begging grounds can we decide? Is the “right” semantics “right” tout court or is it the “right” one with respect to some purpose? Is there only one “right” semantics?) A more direct approach is call ...
Can Modalities Save Naive Set Theory?
... certain views in the philosophy of mathematics and logic, on suitable ways of understanding the qualification “in a special way”. One example is fictionalism, which will be discussed below. For another example, we can understand in a special way as determinately. To motivate this idea, consider an a ...
... certain views in the philosophy of mathematics and logic, on suitable ways of understanding the qualification “in a special way”. One example is fictionalism, which will be discussed below. For another example, we can understand in a special way as determinately. To motivate this idea, consider an a ...
The Expressive Power of Modal Dependence Logic
... With the aim to import dependences and team semantics to modal logic Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, ...
... With the aim to import dependences and team semantics to modal logic Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, ...
Lisp vs Scheme
... • In CL, functions and values have different namespaces. In a form, • car position corresponds to function space • cdr positions correspond to value space • So you can say (flet ((fun (x) (1+ x))) (let ((fun 42)) (fun fun))) ...
... • In CL, functions and values have different namespaces. In a form, • car position corresponds to function space • cdr positions correspond to value space • So you can say (flet ((fun (x) (1+ x))) (let ((fun 42)) (fun fun))) ...
Paper - Department of Computer Science and Information Systems
... et al. 2007]. Basically, the universal box is an S5-box whose accessibility relation contains the accessibility relations for all the other modal operators of the logic. The undecidability result formulated above also applies to those logics where the universal modality is definable, notably to prop ...
... et al. 2007]. Basically, the universal box is an S5-box whose accessibility relation contains the accessibility relations for all the other modal operators of the logic. The undecidability result formulated above also applies to those logics where the universal modality is definable, notably to prop ...
Functional Programming
... same way as tail, except that safetail maps the empty list to the empty list, whereas tail gives an error in this case. Define safetail using: (i) a conditional expression; ...
... same way as tail, except that safetail maps the empty list to the empty list, whereas tail gives an error in this case. Define safetail using: (i) a conditional expression; ...
Lectures on Proof Theory - Create and Use Your home.uchicago
... way of putting it is that R(α) is the result P α (∅) of iterating the PowerSet operation s 7→ P (s) α times, starting with the null set ∅. Then ordinary set theory is a theory of pure well-founded sets and its intended models are structures of the form hR(κ), ∈i, where the numbers κ will depend upo ...
... way of putting it is that R(α) is the result P α (∅) of iterating the PowerSet operation s 7→ P (s) α times, starting with the null set ∅. Then ordinary set theory is a theory of pure well-founded sets and its intended models are structures of the form hR(κ), ∈i, where the numbers κ will depend upo ...