An admissible second order frame rule in region logic
... languages (e.g., [11]), disallowing pointer arithmetic. N.B. We assume the hygiene condition that no variable occurs both bound and free. The grammar is in Fig. 1. As in separation logic, ordinary expressions E do not depend on the heap; command x : = y.f is included for reading a field. Region expr ...
... languages (e.g., [11]), disallowing pointer arithmetic. N.B. We assume the hygiene condition that no variable occurs both bound and free. The grammar is in Fig. 1. As in separation logic, ordinary expressions E do not depend on the heap; command x : = y.f is included for reading a field. Region expr ...
Knowledge Representation and Reasoning
... Typically we even ignore much of the logical structure present in natural language because we are only interested in (or only know how to handle) certain modes of reasoning. For example, for many purposes we can ignore the tense structure of natural language. ...
... Typically we even ignore much of the logical structure present in natural language because we are only interested in (or only know how to handle) certain modes of reasoning. For example, for many purposes we can ignore the tense structure of natural language. ...
ANNALS OF PURE AND APPLIED LOGIC I W
... (programs). The set of formulas is defined as the least set containing ASF and ATF, and such that if f and g are formulas, then so are (-,f ), (,f*), ...
... (programs). The set of formulas is defined as the least set containing ASF and ATF, and such that if f and g are formulas, then so are (-,f ), (,f*), ...
34-2.pdf
... – this proof could have been condensed or simply referenced. 4) Approximation Algorithms. Fundamentals (concepts and classification, stability, dual approximation algorithms), design methods (applied to several problems including cover problems, max cut, knapsack, TSP, and bin-packing), and inapprox ...
... – this proof could have been condensed or simply referenced. 4) Approximation Algorithms. Fundamentals (concepts and classification, stability, dual approximation algorithms), design methods (applied to several problems including cover problems, max cut, knapsack, TSP, and bin-packing), and inapprox ...
Notions of locality and their logical characterizations over nite
... capture complexity classes over classes of (ordered) nite structures, cf. [8, 18]. Since compactness fails in restriction to nite structures [15], to prove results about the limits of expressiveness of rst-order logic, one has to use Ehrenfeucht-Frasse games. Moreover, EhrenfeuchtFrasse gam ...
... capture complexity classes over classes of (ordered) nite structures, cf. [8, 18]. Since compactness fails in restriction to nite structures [15], to prove results about the limits of expressiveness of rst-order logic, one has to use Ehrenfeucht-Frasse games. Moreover, EhrenfeuchtFrasse gam ...
S. P. Odintsov “REDUCTIO AD ABSURDUM” AND LUKASIEWICZ`S
... only first of these two axioms.. In this way minimal logic is paraconsistent according to the generally accepted definition of paraconsistent logics as logics admitting inconsistent but non-trivial theories. But it lies on the border line of paraconsistency. Usually (see, e.g. [27]) the above definitio ...
... only first of these two axioms.. In this way minimal logic is paraconsistent according to the generally accepted definition of paraconsistent logics as logics admitting inconsistent but non-trivial theories. But it lies on the border line of paraconsistency. Usually (see, e.g. [27]) the above definitio ...
A Mathematical Introduction to Modal Logic
... The binding strength of the symbols will be as same as in the propositional logic. The additional symbol ♦ will bind strongest. Thus, we will omit the parenthesis where there is no ambiguity. Exercise 2.1. Verify that the following are well-formed formulae in the language of modal logic: (i) ♦♦♦p, ( ...
... The binding strength of the symbols will be as same as in the propositional logic. The additional symbol ♦ will bind strongest. Thus, we will omit the parenthesis where there is no ambiguity. Exercise 2.1. Verify that the following are well-formed formulae in the language of modal logic: (i) ♦♦♦p, ( ...
The Natural Order-Generic Collapse for ω
... to first-order logic with linear ordering alone. A recent overview of this area of research is given in [3]. In classical database theory, attention usually is restricted to finite databases. In this setting Benedikt et al. [2] have obtained a strong collapse result: Firstorder logic has the natural o ...
... to first-order logic with linear ordering alone. A recent overview of this area of research is given in [3]. In classical database theory, attention usually is restricted to finite databases. In this setting Benedikt et al. [2] have obtained a strong collapse result: Firstorder logic has the natural o ...
Formal Reasoning - Institute for Computing and Information Sciences
... The sentence ‘if a and b, then a’ is true, whatever you substitute for a and b. So, we’d like to be able to say: the sentence ‘a ∧ b → a’ is true2 . But we can’t, because we haven’t formally defined what that means yet. As of yet, ‘a ∧ b → a’ is only one of the words of our formal language. Which is ...
... The sentence ‘if a and b, then a’ is true, whatever you substitute for a and b. So, we’d like to be able to say: the sentence ‘a ∧ b → a’ is true2 . But we can’t, because we haven’t formally defined what that means yet. As of yet, ‘a ∧ b → a’ is only one of the words of our formal language. Which is ...
Pseudo-finite model theory
... (–categorical for each ) theories are pseudo-finite. For a stability theoretic analysis of pseudo-finite structures, see [10] and [4]. We use common model theoretic notation, as e.g. in [9]. When we talk about finite structures we do not assume that the vocabulary is necessarily finite. ...
... (–categorical for each ) theories are pseudo-finite. For a stability theoretic analysis of pseudo-finite structures, see [10] and [4]. We use common model theoretic notation, as e.g. in [9]. When we talk about finite structures we do not assume that the vocabulary is necessarily finite. ...
article in press - School of Computer Science
... account for conditions which involve more than one guard relation. We believe that this method is particularly promising for intuitionistic modal logic, where there exists a variety of systems, most of them semantically defined, with various conditions connecting the intuitionistic and modal accessi ...
... account for conditions which involve more than one guard relation. We believe that this method is particularly promising for intuitionistic modal logic, where there exists a variety of systems, most of them semantically defined, with various conditions connecting the intuitionistic and modal accessi ...
The Expressive Power of Modal Dependence Logic
... logics with team semantics has been active, see e.g. [3,4,5,6,12,13,15,18]. An important logic, closely related to modal dependence logic, is modal logic with intuitionistic disjunction, ML(>). It was already observed by Väänänen [17] that dependence atoms can be defined by using the intuitionistic ...
... logics with team semantics has been active, see e.g. [3,4,5,6,12,13,15,18]. An important logic, closely related to modal dependence logic, is modal logic with intuitionistic disjunction, ML(>). It was already observed by Väänänen [17] that dependence atoms can be defined by using the intuitionistic ...
vmcai - of Philipp Ruemmer
... arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based on a sequent calculus, the proof rules are extended by labelled formulae and anno ...
... arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based on a sequent calculus, the proof rules are extended by labelled formulae and anno ...
Complexity of Recursive Normal Default Logic 1. Introduction
... propositional logic nonmonotonic formalisms, the basic results are found in [BF91, MT91, Got92, Van89]. In case of formalisms admitting variables and, more generally, infinite recursive propositional nonmonotonic formalisms, a number of results has been found. These include basic complexity results ...
... propositional logic nonmonotonic formalisms, the basic results are found in [BF91, MT91, Got92, Van89]. In case of formalisms admitting variables and, more generally, infinite recursive propositional nonmonotonic formalisms, a number of results has been found. These include basic complexity results ...
A BRIEF INTRODUCTION TO MODAL LOGIC Introduction Consider
... Schema K For any wffs α and β, we will assume that (α =⇒ β) =⇒ (α =⇒ β). Our proof system will also have two rules of inference. Definition 2.7. A ‘rule of inference’ is an ordered pair (Γ, α), where Γ is a set of wffs and α is a single wff. If the propositions of Γ are theorems of the system, so ...
... Schema K For any wffs α and β, we will assume that (α =⇒ β) =⇒ (α =⇒ β). Our proof system will also have two rules of inference. Definition 2.7. A ‘rule of inference’ is an ordered pair (Γ, α), where Γ is a set of wffs and α is a single wff. If the propositions of Γ are theorems of the system, so ...
![overhead 8/singular sentences [ov]](http://s1.studyres.com/store/data/009258618_1-2a98e952bde8fd34c716ae0716ce6df4-300x300.png)
overhead 8/singular sentences [ov]
... subjects of these sentences - but these words are different from names in that they don't refer: "something" and "everything" don't refer to particular things or people; obviously "nothing" doesn't refer ...
... subjects of these sentences - but these words are different from names in that they don't refer: "something" and "everything" don't refer to particular things or people; obviously "nothing" doesn't refer ...
Introduction to Discrete Structures Introduction
... • Sometimes we need to consider ordered collections of objects • Definition: The ordered n-tuple (a1,a2,…,an) is the ordered collection with the element ai being the i-th element for i=1,2,…,n • Two ordered n-tuples (a1,a2,…,an) and (b1,b2,…,bn) are equal if and only if for every i=1,2,…,n we have a ...
... • Sometimes we need to consider ordered collections of objects • Definition: The ordered n-tuple (a1,a2,…,an) is the ordered collection with the element ai being the i-th element for i=1,2,…,n • Two ordered n-tuples (a1,a2,…,an) and (b1,b2,…,bn) are equal if and only if for every i=1,2,…,n we have a ...
Strong Completeness and Limited Canonicity for PDL
... i.e. when | ϕ implies that there is a finite ⊆ with | ϕ, hence | → ϕ. This is, for example, the case in propositional and predicate logic, and in many modal logics such as K and S5. Segerberg’s axiomatization of PDL is only weakly complete, since PDL is not compact: we have that {[a ...
... i.e. when | ϕ implies that there is a finite ⊆ with | ϕ, hence | → ϕ. This is, for example, the case in propositional and predicate logic, and in many modal logics such as K and S5. Segerberg’s axiomatization of PDL is only weakly complete, since PDL is not compact: we have that {[a ...
The Complete Proof Theory of Hybrid Systems
... prove is true. Soundness should be sine qua non for formal verification, but is so complex for hybrid systems [7], [27] that it is often inadvertently forsaken. In logic, we can simply ensure soundness by checking it locally per proof rule. More intriguingly, however, our logical setting also enable ...
... prove is true. Soundness should be sine qua non for formal verification, but is so complex for hybrid systems [7], [27] that it is often inadvertently forsaken. In logic, we can simply ensure soundness by checking it locally per proof rule. More intriguingly, however, our logical setting also enable ...
Symbolic Execution - Harvard University
... he language that we will use for writing assertion is the set of logical formulas that include ons of arithmetic expressions, standard logical operators (and, or, implication, negation), as w ifiers (universal and existential). Assertions may use additional logical variables, different tha ...
... he language that we will use for writing assertion is the set of logical formulas that include ons of arithmetic expressions, standard logical operators (and, or, implication, negation), as w ifiers (universal and existential). Assertions may use additional logical variables, different tha ...
Nonmonotonic Reasoning - Computer Science Department
... by usual type reasoning systems, except that the rules carry the list of “exceptional cases” making the application of such rule invalid. Formally, Reiter, [25] introduced the concept of default theory. A default theory is a pair hD, W i where W is a set of sentences of the underlying language L and ...
... by usual type reasoning systems, except that the rules carry the list of “exceptional cases” making the application of such rule invalid. Formally, Reiter, [25] introduced the concept of default theory. A default theory is a pair hD, W i where W is a set of sentences of the underlying language L and ...
From Syllogism to Common Sense Normal Modal Logic
... ‣ “ If it never rains in Copenhagen, then Elvis never died.” ‣ (No variables are shared in example => relevant implication) ‣ For strict implication, we define A ~~> B by [] (A --> B) ‣ These systems are however mutually incompatible, and no base logic was given of which the other logics are extensi ...
... ‣ “ If it never rains in Copenhagen, then Elvis never died.” ‣ (No variables are shared in example => relevant implication) ‣ For strict implication, we define A ~~> B by [] (A --> B) ‣ These systems are however mutually incompatible, and no base logic was given of which the other logics are extensi ...
a Decidable Language Supporting Syntactic Query Difference
... with negation of extensional predicates within their bodies(CQ ) may also be decided[14]. The 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 conjun ...
... with negation of extensional predicates within their bodies(CQ ) may also be decided[14]. The 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 conjun ...
Completeness - OSU Department of Mathematics
... • Whenever f is an n-ary function symbol h(f A (a1 , . . . , an )) = f B (h(a1 ), . . . , h(an )) for all a1 , . . . , an ∈ |A|. Notice that if = is in L, A and B respect equality and h is a homormorphism of A to B then h is 1-1 i.e. h is an embedding of A into B. When h is a homomorphism from A to ...
... • Whenever f is an n-ary function symbol h(f A (a1 , . . . , an )) = f B (h(a1 ), . . . , h(an )) for all a1 , . . . , an ∈ |A|. Notice that if = is in L, A and B respect equality and h is a homormorphism of A to B then h is 1-1 i.e. h is an embedding of A into B. When h is a homomorphism from A to ...
Can Modalities Save Naive Set Theory?
... its extensions. In response, one could use two different modal operators in (2Comp2), but since this drastically increases the space of available options, we don’t consider it here. Instead, we explore the more restricted option of replacing the second occurrence of 2 in (2Comp2) by a string of moda ...
... its extensions. In response, one could use two different modal operators in (2Comp2), but since this drastically increases the space of available options, we don’t consider it here. Instead, we explore the more restricted option of replacing the second occurrence of 2 in (2Comp2) by a string of moda ...