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, ...
A sequent calculus demonstration of Herbrand`s Theorem
... a construction yielding, from a cut-free GS proof of a formula Γ, an Herbrand proof of Γ; thus the general Herbrand’s theorem is shown to be a corollary of the general cut-elimination for the first-order classical sequent calculus, rather than of the midesequent theorem. We prove this by showing th ...
... a construction yielding, from a cut-free GS proof of a formula Γ, an Herbrand proof of Γ; thus the general Herbrand’s theorem is shown to be a corollary of the general cut-elimination for the first-order classical sequent calculus, rather than of the midesequent theorem. We prove this by showing th ...
Using Modal Logics to Express and Check Global Graph Properties
... then use these results to prove that a certain property cannot be expressed by any formula in the basic graph logic. To do this, we take two frames that are “similar” and show that in one the desired property holds, while in the other it does not. We present two of these “similarity” results (more d ...
... then use these results to prove that a certain property cannot be expressed by any formula in the basic graph logic. To do this, we take two frames that are “similar” and show that in one the desired property holds, while in the other it does not. We present two of these “similarity” results (more d ...
The Dedekind Reals in Abstract Stone Duality
... either aborts or never halts. The basic process whereby this is done is unification, in which variables are assigned values according to the constraints imposed by the rest of the program, i.e. the values that they must have if the program is ever to terminate with a proof of the original predicate. ...
... either aborts or never halts. The basic process whereby this is done is unification, in which variables are assigned values according to the constraints imposed by the rest of the program, i.e. the values that they must have if the program is ever to terminate with a proof of the original predicate. ...
A Survey on Small Fragments of First-Order Logic over Finite
... ferent characterizations are known than for star-free languages. The algebraic counterpart is the class DA of finite monoids. The first letter D stands for one of Green’s relations [25] and the second letter comes from Aperiodic. Schützenberger has characterized DA by unambiguous polynomials which ...
... ferent characterizations are known than for star-free languages. The algebraic counterpart is the class DA of finite monoids. The first letter D stands for one of Green’s relations [25] and the second letter comes from Aperiodic. Schützenberger has characterized DA by unambiguous polynomials which ...
lecture6.1
... She chooses two (large) prime numbers, p and q and computes n=pq and (n) . [“large” =512 bits +] She chooses a number e such that e is relatively prime to (n) and computes d, the inverse of ...
... She chooses two (large) prime numbers, p and q and computes n=pq and (n) . [“large” =512 bits +] She chooses a number e such that e is relatively prime to (n) and computes d, the inverse of ...
A Resolution-Based Proof Method for Temporal Logics of
... This paper presents two logics, called KLn and BLn respectively, and gives resolutionbased proof methods for both. The logic KLn is a temporal logic of knowledge. That is, in addition to the usual connectives of linear discrete temporal logic [4], KLn contains an indexed set of unary modal connectiv ...
... This paper presents two logics, called KLn and BLn respectively, and gives resolutionbased proof methods for both. The logic KLn is a temporal logic of knowledge. That is, in addition to the usual connectives of linear discrete temporal logic [4], KLn contains an indexed set of unary modal connectiv ...
Formal logic
... But how and why can we conclude that this last sentence follows from the previous two premises? Or, more generally, how can we determine whether a formula ϕ is a valid consequence of a set of formulas {ϕ1 , . . . , ϕn }? Modern logic offers two possible ways, that used to be fused in the time of syl ...
... But how and why can we conclude that this last sentence follows from the previous two premises? Or, more generally, how can we determine whether a formula ϕ is a valid consequence of a set of formulas {ϕ1 , . . . , ϕn }? Modern logic offers two possible ways, that used to be fused in the time of syl ...
Elementary Logic
... A countable set of function symbols with associated ranks (arities); A countable set of constants (which may be seen as functions with rank 0); A countable set of predicate symbols with associated ranks (arities); ...
... A countable set of function symbols with associated ranks (arities); A countable set of constants (which may be seen as functions with rank 0); A countable set of predicate symbols with associated ranks (arities); ...
Multiverse Set Theory and Absolutely Undecidable Propositions
... puts so much weight on categoricity. Indeed, if set theory had a categorical axiomatization, the categoricity proof itself, carried out in set theory, would be meaningful. But with non-categoricity everything is lost.8 For a time Gödel contemplated the idea that there could be absolutely undecidabl ...
... puts so much weight on categoricity. Indeed, if set theory had a categorical axiomatization, the categoricity proof itself, carried out in set theory, would be meaningful. But with non-categoricity everything is lost.8 For a time Gödel contemplated the idea that there could be absolutely undecidabl ...
EMBEDDING AN ANALYTIC EQUIVALENCE RELATION IN THE
... iff it is closed in N × N .) In subsequent discussions, subsets of these subspaces will be characterized (for example, as being closed) without mentioning the subspace. Theorem 2.1. If E ⊆ X × X is a Σ11 equivalence relation, then there are equivalence relations I and J on N × N , each of which has ...
... iff it is closed in N × N .) In subsequent discussions, subsets of these subspaces will be characterized (for example, as being closed) without mentioning the subspace. Theorem 2.1. If E ⊆ X × X is a Σ11 equivalence relation, then there are equivalence relations I and J on N × N , each of which has ...
degrees of recursively saturated models
... 0. Introduction. The classic theorem of Tennenbaum [T] says that there is no recursive nonstandard model of Peano arithmetic. Indeed, if (u, ffi, 0) N P, and (to, ffi, O) is nonstandard, then neither © nor O is recursive. In the above situation, (w, ffi) and («, O) are recursively saturated, and now ...
... 0. Introduction. The classic theorem of Tennenbaum [T] says that there is no recursive nonstandard model of Peano arithmetic. Indeed, if (u, ffi, 0) N P, and (to, ffi, O) is nonstandard, then neither © nor O is recursive. In the above situation, (w, ffi) and («, O) are recursively saturated, and now ...
![overhead 12/proofs in predicate logic [ov]](http://s1.studyres.com/store/data/011612593_1-f0437b45ca3df4f633ddcc6197d427a6-300x300.png)
overhead 12/proofs in predicate logic [ov]
... Existential Instantiation (EI) (final version) (x)x provided we flag a a - the flagging is just to help us identify use of individual constants so that we can apply the following restriction: R1 A letter being flagged must be new to the proof, that is, it may not appear, either in a formula or as ...
... Existential Instantiation (EI) (final version) (x)x provided we flag a a - the flagging is just to help us identify use of individual constants so that we can apply the following restriction: R1 A letter being flagged must be new to the proof, that is, it may not appear, either in a formula or as ...
THE ABUNDANCE OF THE FUTURE A Paraconsistent Approach to
... this view has never been deeply investigated, and this is probably due to its contradictory flavor. Indeed, this position is naturally embodied by a paraconsistent semantics (Section 4). Can this possibly make sense or it is just a “weird” conceptual alternative among all the possible temporal logic ...
... this view has never been deeply investigated, and this is probably due to its contradictory flavor. Indeed, this position is naturally embodied by a paraconsistent semantics (Section 4). Can this possibly make sense or it is just a “weird” conceptual alternative among all the possible temporal logic ...
Math 320 Course Notes Chapter 7
... Theorem 3.6 The set Q of rational numbers is countable. Proof: First write Q = Q+ [ f0g [ Q ; where Q+ and Q denote the sets of positive and negative rational numbers respectively. By mapping q to q, we see that Q+ Q : Hence if we show that Q+ is countable, and apply Theorem 3.5.1 we get that Q is ...
... Theorem 3.6 The set Q of rational numbers is countable. Proof: First write Q = Q+ [ f0g [ Q ; where Q+ and Q denote the sets of positive and negative rational numbers respectively. By mapping q to q, we see that Q+ Q : Hence if we show that Q+ is countable, and apply Theorem 3.5.1 we get that Q is ...
Everything is Knowable - Computer Science Intranet
... cannot be believed after being announced. Both are quite different from Moore’s original analysis that p ∧ ¬Kp cannot be sincerely announced/uttered! Unlike the single-agent version, the multi-agent version of the Moore-sentence is not problematic. If I tell you “You don’t know that I play the cello ...
... cannot be believed after being announced. Both are quite different from Moore’s original analysis that p ∧ ¬Kp cannot be sincerely announced/uttered! Unlike the single-agent version, the multi-agent version of the Moore-sentence is not problematic. If I tell you “You don’t know that I play the cello ...
Intuitionistic Logic - Institute for Logic, Language and Computation
... • A proof of φ ∨ ψ consists of a proof of φ or a proof of ψ plus a conclusion φ ∨ ψ, • A proof of φ → ψ consists of a method of converting any proof of φ into a proof of ψ, • No proof of ⊥ exists, • A proof of ∃x φ(x) consists of a name d of an object constructed in the intended domain of discourse ...
... • A proof of φ ∨ ψ consists of a proof of φ or a proof of ψ plus a conclusion φ ∨ ψ, • A proof of φ → ψ consists of a method of converting any proof of φ into a proof of ψ, • No proof of ⊥ exists, • A proof of ∃x φ(x) consists of a name d of an object constructed in the intended domain of discourse ...
From Ramsey Theory to arithmetic progressions and hypergraphs
... k-simplices, then it is possible to remove at most ank edges from H to make it k-simplex-free. A corollary to the removal lemma above is that we get an effective bound for n in the Furstenberg-Katznelson theorem. ...
... k-simplices, then it is possible to remove at most ank edges from H to make it k-simplex-free. A corollary to the removal lemma above is that we get an effective bound for n in the Furstenberg-Katznelson theorem. ...
Automata-Theoretic Model Checking Lili Anne Dworkin Advised by Professor Steven Lindell
... The strategy outlined above depends on a few key results, including that temporal logic formulas can be converted into an automaton over infinite words, and that these automata are closed under intersection. Thus, a great deal of this paper is dedicated to exploring the properties and relative expre ...
... The strategy outlined above depends on a few key results, including that temporal logic formulas can be converted into an automaton over infinite words, and that these automata are closed under intersection. Thus, a great deal of this paper is dedicated to exploring the properties and relative expre ...
Proof Search in Modal Logic
... 1.2.1 Formal systems and provability Peano Arithmetic (PA) is a formal system whose axioms are the axioms of classical firstorder logic (including those for falsum), axioms for zero and successor, recursion axioms for addition and multiplication, and the induction axiom scheme. PA’s inference rules ...
... 1.2.1 Formal systems and provability Peano Arithmetic (PA) is a formal system whose axioms are the axioms of classical firstorder logic (including those for falsum), axioms for zero and successor, recursion axioms for addition and multiplication, and the induction axiom scheme. PA’s inference rules ...
Document
... Any valid argument form can be used • there are infinitely many of them, based on different tautologies • validity of an argument form can be verified e.g. using truth tables There are simple, commonly used and useful argument forms • when writing proofs for humans, it is good to use well known ...
... Any valid argument form can be used • there are infinitely many of them, based on different tautologies • validity of an argument form can be verified e.g. using truth tables There are simple, commonly used and useful argument forms • when writing proofs for humans, it is good to use well known ...
Syllogistic Logic with Complements
... Figure 1: Syllogistic logic with complement. Proof trees We have discussed the meager syntax of L(all, some, 0 ) and its semantics. We next turn to the proof theory. A proof tree over Γ is a finite tree T whose nodes are labeled with sentences in our fragment, with the additional property that each ...
... Figure 1: Syllogistic logic with complement. Proof trees We have discussed the meager syntax of L(all, some, 0 ) and its semantics. We next turn to the proof theory. A proof tree over Γ is a finite tree T whose nodes are labeled with sentences in our fragment, with the additional property that each ...
Classical Logic and the Curry–Howard Correspondence
... The rest of mathematics was to be reconstructed on this basis using purely constructive techniques (see e.g. [Dum00]). Brouwer’s doctrines, and the work by Heyting and Kolmogorov [Kol67] on intuitionistic logic, gave rise to a constructive interpretation of the logical connectives that has become st ...
... The rest of mathematics was to be reconstructed on this basis using purely constructive techniques (see e.g. [Dum00]). Brouwer’s doctrines, and the work by Heyting and Kolmogorov [Kol67] on intuitionistic logic, gave rise to a constructive interpretation of the logical connectives that has become st ...
Possible Worlds, The Lewis Principle, and the Myth of a Large
... Lewis’s Conception of Worlds Worlds are mereological sums of spatiotemporal objects. Worlds are maximal in the following sense: if x is a world, then any object that bears any (positive) spatiotemporal relation to x is part of x. The actual world is the world of which we are a part. There are worlds ...
... Lewis’s Conception of Worlds Worlds are mereological sums of spatiotemporal objects. Worlds are maximal in the following sense: if x is a world, then any object that bears any (positive) spatiotemporal relation to x is part of x. The actual world is the world of which we are a part. There are worlds ...
A BRIEF INTRODUCTION TO MODAL LOGIC Introduction Consider
... Classical Tautologies All valid formula of PC (that is, all the tautologies of traditional propositional logic) will be taken as axioms. 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 infe ...
... Classical Tautologies All valid formula of PC (that is, all the tautologies of traditional propositional logic) will be taken as axioms. 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 infe ...