Automata, Languages, and Programming
... It is known that the algebra of regular sets Reg Σ ∗ is the free Kleene algebra generated by Σ [18]. This is equivalent to the completeness of the axioms of KA for the standard language interpretation R of regular expressions. That is, for any two regular expressions e1 , e2 over Σ, if R(e1 ) = R(e2 ...
... It is known that the algebra of regular sets Reg Σ ∗ is the free Kleene algebra generated by Σ [18]. This is equivalent to the completeness of the axioms of KA for the standard language interpretation R of regular expressions. That is, for any two regular expressions e1 , e2 over Σ, if R(e1 ) = R(e2 ...
Polarizing Double-Negation Translations
... two multisets of formulæ and a distinguished set (the stoup) containing zero or one formula. It will be noted Γ ⊢ A; ∆ when the distinguished set contains a formula A, and Γ ⊢ .; ∆ when it contains no formula. The focused sequent calculus we define serves our particular purpose; for instance it is n ...
... two multisets of formulæ and a distinguished set (the stoup) containing zero or one formula. It will be noted Γ ⊢ A; ∆ when the distinguished set contains a formula A, and Γ ⊢ .; ∆ when it contains no formula. The focused sequent calculus we define serves our particular purpose; for instance it is n ...
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 ...
Guarded negation
... as a syntactic fragment of first-order logic, it is also natural to ask for syntactic explanations: what syntactic features of modal formulas (viewed as first-order formulas) are responsible for their good behavior? And can we generalize modal logic, preserving these features, while at the same tim ...
... as a syntactic fragment of first-order logic, it is also natural to ask for syntactic explanations: what syntactic features of modal formulas (viewed as first-order formulas) are responsible for their good behavior? And can we generalize modal logic, preserving these features, while at the same tim ...
on the Complexity of Quantifier-Free Fixed-Size Bit-Vector
... Lemma 2. QF BV2!1 can be (polynomially) reduced to Sequential Circuits. Proof. In [10,15], the authors give a translation from quantifier-free Presburger arithmetic with bitwise operations (QFPAbit) to Sequential Circuits. We can adopt their approach in order to construct a translation for QF BV2!1 ...
... Lemma 2. QF BV2!1 can be (polynomially) reduced to Sequential Circuits. Proof. In [10,15], the authors give a translation from quantifier-free Presburger arithmetic with bitwise operations (QFPAbit) to Sequential Circuits. We can adopt their approach in order to construct a translation for QF BV2!1 ...
Logic for Computer Science. Lecture Notes
... otherwise select (nondeterministically) a set of axioms or previously proved theorems and then apply a nondeterministically chosen applicable derivation rule. Accept the thus obtained conclusion as the new theorem and repeat the described procedure. As axioms are special kinds of derivation rules (n ...
... otherwise select (nondeterministically) a set of axioms or previously proved theorems and then apply a nondeterministically chosen applicable derivation rule. Accept the thus obtained conclusion as the new theorem and repeat the described procedure. As axioms are special kinds of derivation rules (n ...
- Horn-Representation of a Concept Lattice,
... ∧-closure of RK . By Proposition 1, R̂K can be represented by the Horn formula FK consisting of its prime implicates. This formula is the Horn representation of the concept lattice we wanted to derive. Definition Horn representation: Let C1 , C2 , . . . , Ck be the prime implicates of R̂K . The form ...
... ∧-closure of RK . By Proposition 1, R̂K can be represented by the Horn formula FK consisting of its prime implicates. This formula is the Horn representation of the concept lattice we wanted to derive. Definition Horn representation: Let C1 , C2 , . . . , Ck be the prime implicates of R̂K . The form ...
Epsilon Substitution for Transfinite Induction
... ∀x((∀y < xφ[y]) → φ[x]) → ∀xφ[x] in place of the usual induction axiom ∀x(φ[x] → φ[Sx]) → ∀x As a preliminary step, he proves termination for first order arithmetic with the complete induction axiom using ordinal assignments in the style of [Ackermann, 1940]. This has the added advantage of allowing ...
... ∀x((∀y < xφ[y]) → φ[x]) → ∀xφ[x] in place of the usual induction axiom ∀x(φ[x] → φ[Sx]) → ∀x As a preliminary step, he proves termination for first order arithmetic with the complete induction axiom using ordinal assignments in the style of [Ackermann, 1940]. This has the added advantage of allowing ...
On Natural Deduction in Classical First-Order Logic: Curry
... The two most successful and most studied deductive systems for first-order logic are Gentzen’s natural deduction [28] and Gentzen’s sequent calculus [16, 15]. The first elegant constructive proof of Herbrand’s Theorem was indeed obtained as a corollary of Gentzen’s Cut elimination Theorem. Today, th ...
... The two most successful and most studied deductive systems for first-order logic are Gentzen’s natural deduction [28] and Gentzen’s sequent calculus [16, 15]. The first elegant constructive proof of Herbrand’s Theorem was indeed obtained as a corollary of Gentzen’s Cut elimination Theorem. Today, th ...
Completeness and Decidability of a Fragment of Duration Calculus
... Duration Calculus (DC) was introduced by Zhou, Hoare and Ravn in 1991 as a logic to specify the requirements for real-time systems. DC has been used successfully in many case studies, see e.g. [ZZ94,YWZP94,HZ94,DW94,BHCZ94,XH95], [Dan98,ED99]. In [DW94], we have developed a method for designing a re ...
... Duration Calculus (DC) was introduced by Zhou, Hoare and Ravn in 1991 as a logic to specify the requirements for real-time systems. DC has been used successfully in many case studies, see e.g. [ZZ94,YWZP94,HZ94,DW94,BHCZ94,XH95], [Dan98,ED99]. In [DW94], we have developed a method for designing a re ...
ON PRESERVING 1. Introduction The
... common underlying language) then they must agree on which sets are consistent and which are inconsistent. For consider, if conX (Γ) and Y preserves the X consistency predicate then conX (CY (Γ)). Suppose that Γ is not Y -consistent, then CY (Γ) = S. By [R] CX (CY (Γ)) = CX (S) = S which is to say th ...
... common underlying language) then they must agree on which sets are consistent and which are inconsistent. For consider, if conX (Γ) and Y preserves the X consistency predicate then conX (CY (Γ)). Suppose that Γ is not Y -consistent, then CY (Γ) = S. By [R] CX (CY (Γ)) = CX (S) = S which is to say th ...
Logic and Resolution - Institute for Computing and Information
... If P is a unary predicate symbol and x is a variable, then P (x) is an atom. Q(f (y), c, g(f (x), z)) is an atom if Q is a ternary predicate symbol, c is a constant, f a unary function symbol, g a binary function symbol, and x, y and z are variables. For the same predicate symbols P and Q, P (Q) is ...
... If P is a unary predicate symbol and x is a variable, then P (x) is an atom. Q(f (y), c, g(f (x), z)) is an atom if Q is a ternary predicate symbol, c is a constant, f a unary function symbol, g a binary function symbol, and x, y and z are variables. For the same predicate symbols P and Q, P (Q) is ...
A really temporal logic
... TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable present a tableau-based decision procedure and a model-checking ...
... TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable present a tableau-based decision procedure and a model-checking ...
Translating the Hypergame Paradox - UvA-DARE
... that xRi iff z E A. Indeed, if {x/xRi} s A, then i E domA z A but i +! {x/xRi} b ecause A n D = 0. Adapted to the relation EJ of Example 3, this argument proves that every set in 1 is productive, with the identity map as a productive function. Actually, in recursion theory it is not hard to prove mo ...
... that xRi iff z E A. Indeed, if {x/xRi} s A, then i E domA z A but i +! {x/xRi} b ecause A n D = 0. Adapted to the relation EJ of Example 3, this argument proves that every set in 1 is productive, with the identity map as a productive function. Actually, in recursion theory it is not hard to prove mo ...
admissible and derivable rules in intuitionistic logic
... A1 , . . . , An C, iff the set of theorems of L is closed under this rule, or equivalently iff for every substitution s of propositional formulae for propositional constants: if `L s(A1 ), . . . , `L s(An ), then `L s(C). This rule is said to be a derivable rule in L iff: `L A1 , . . . , An , → C. ...
... A1 , . . . , An C, iff the set of theorems of L is closed under this rule, or equivalently iff for every substitution s of propositional formulae for propositional constants: if `L s(A1 ), . . . , `L s(An ), then `L s(C). This rule is said to be a derivable rule in L iff: `L A1 , . . . , An , → C. ...
OF CONCEPTUAL GRAPHS - Tampereen yliopisto
... In order to see if conceptual graphs are more simple, have more deductive power or have more expressional power than FOPL, we shall carry out an extensive comparison between FOPL and conceptual graphs in sections 3 and 4. To make the comparison more easy, we use simplified forms of both FOPL and co ...
... In order to see if conceptual graphs are more simple, have more deductive power or have more expressional power than FOPL, we shall carry out an extensive comparison between FOPL and conceptual graphs in sections 3 and 4. To make the comparison more easy, we use simplified forms of both FOPL and co ...
Sample pages 2 PDF
... that formalize computations. In both cases, we need to define the syntax and the semantics. The syntax defines what strings of symbols constitute legal formulas (legal programs, in the case of languages), while the semantics defines what legal formulas mean (what legal programs compute). Once the sy ...
... that formalize computations. In both cases, we need to define the syntax and the semantics. The syntax defines what strings of symbols constitute legal formulas (legal programs, in the case of languages), while the semantics defines what legal formulas mean (what legal programs compute). Once the sy ...
Notions of locality and their logical characterizations over nite
... suggested by Fagin, Stockmeyer and Vardi in [11] to build a library of winning strategies for those games. Or, more generally, one would like to have a collection of versatile and easily applicable tools for proving expressibility bounds for rst-order logic. A number of results proving expressibili ...
... suggested by Fagin, Stockmeyer and Vardi in [11] to build a library of winning strategies for those games. Or, more generally, one would like to have a collection of versatile and easily applicable tools for proving expressibility bounds for rst-order logic. A number of results proving expressibili ...
ND for predicate logic ∀-elimination, first attempt Variable capture
... In the conclusion of each rule, the formula not in the context is called the main formula or principal formula. In the rule Ax , both occurrences of A are principal. ...
... In the conclusion of each rule, the formula not in the context is called the main formula or principal formula. In the rule Ax , both occurrences of A are principal. ...
A New Decidability Technique for Ground Rewrite Systems with Applications
... In this article, we develop a standard form for ground rewrite systems and the concept of standard rewriting. The concepts are then used to: prove a pumping lemma for them, and to derive a new and direct decidability technique for decision problems of ground rewrite systems. We then apply these conc ...
... In this article, we develop a standard form for ground rewrite systems and the concept of standard rewriting. The concepts are then used to: prove a pumping lemma for them, and to derive a new and direct decidability technique for decision problems of ground rewrite systems. We then apply these conc ...
the theory of form logic - University College Freiburg
... and Wittgenstein, nor even to decide whether it is an appropriate dispute in the present context. The mere possibility of disagreement concerning the question of the logical form of atomic propositions suggests that the PL-syntax of atomic formulas is not indisputable. Alternative logical systems ar ...
... and Wittgenstein, nor even to decide whether it is an appropriate dispute in the present context. The mere possibility of disagreement concerning the question of the logical form of atomic propositions suggests that the PL-syntax of atomic formulas is not indisputable. Alternative logical systems ar ...
CHAPTER 1 The main subject of Mathematical Logic is
... for their average. It is possible to “extract” this algorithm from the formalized proof. This extract will be a term of the underlying logical language. However, for efficiency reasons one may later translate it into a functional programming language (like Scheme or Haskell). An obvious advantage of ...
... for their average. It is possible to “extract” this algorithm from the formalized proof. This extract will be a term of the underlying logical language. However, for efficiency reasons one may later translate it into a functional programming language (like Scheme or Haskell). An obvious advantage of ...
Lecture 9 Notes
... the next. Finding an elegant representation of the proof system of tableaux leads us even further. There are more steps that one could go if one were to build an efficient proof system in a computer, but we’ll get to that later. The current form is the most appropirate one for another important task ...
... the next. Finding an elegant representation of the proof system of tableaux leads us even further. There are more steps that one could go if one were to build an efficient proof system in a computer, but we’ll get to that later. The current form is the most appropirate one for another important task ...
Modal_Logics_Eyal_Ariel_151107
... Let L(σ) be a first order language. When is a formula true? A Structure M is a pair M=, such that –
D – (domain) a non-empty set of objects.
I – an interpretation function of σ:
...
... Let L(σ) be a first order language. When is a formula true? A Structure M is a pair M=