Knowledge Representation: Logic
... so the code must be rewritten. The elements of the map could be associated with object classes divided into point-like, line-like and so on. Addition of a new component may be then achieved by adding a new subclass, but it can be impossible, for example for street names. We may as well express the c ...
... so the code must be rewritten. The elements of the map could be associated with object classes divided into point-like, line-like and so on. Addition of a new component may be then achieved by adding a new subclass, but it can be impossible, for example for street names. We may as well express the c ...
Homogeneous structures, ω-categoricity and amalgamation
... homogeneous L-structure. Suppose further that for each n ∈ N, there are finitely many isomorphism types of substructures of M with n elements. Then M is ω-categorical. Proof. This will follow from the Ryll-Nardzewski Theorem below, but it’s perhaps instructive to give a direct proof. For simplicity ...
... homogeneous L-structure. Suppose further that for each n ∈ N, there are finitely many isomorphism types of substructures of M with n elements. Then M is ω-categorical. Proof. This will follow from the Ryll-Nardzewski Theorem below, but it’s perhaps instructive to give a direct proof. For simplicity ...
Thesis Proposal: A Logical Foundation for Session-based
... The core idea of session types is to structure communication between processes around the concept of a session. A (binary) session consists of a description of the interactive behavior between two components of a concurrent system, with an intrinsic notion of duality: When one component sends, the o ...
... The core idea of session types is to structure communication between processes around the concept of a session. A (binary) session consists of a description of the interactive behavior between two components of a concurrent system, with an intrinsic notion of duality: When one component sends, the o ...
relevant reasoning as the logical basis of
... the notion of entailment is represented by the extensional notion of material implication (denoted by → in this paper) which is defined as A→B =df ¬(A∧¬B) or A→B =df ¬A∨B. However, the material implication is just a truth-function of its antecedent and consequent but not requires that there must exi ...
... the notion of entailment is represented by the extensional notion of material implication (denoted by → in this paper) which is defined as A→B =df ¬(A∧¬B) or A→B =df ¬A∨B. However, the material implication is just a truth-function of its antecedent and consequent but not requires that there must exi ...
higher-order logic - University of Amsterdam
... new characterization results. For instance, Lindström himself proved that elementary logic is also the strongest logic with an effective finitary syntax to possess the Löwenheim-Skolem property and be complete. (The infinitary language L!1 ! has both, without collapsing into elementary logic, howe ...
... new characterization results. For instance, Lindström himself proved that elementary logic is also the strongest logic with an effective finitary syntax to possess the Löwenheim-Skolem property and be complete. (The infinitary language L!1 ! has both, without collapsing into elementary logic, howe ...
On Dummett`s Pragmatist Justification Procedure
... Here, Dummett assumes that the minor premiss A is atomic. This assumption is essential, because, according to Dummett’s original definition, a canonical argument must have an atomic conclusion. Prawitz’s counterexample is basically the same (Dummett’s example being an instance thereof) with the dif ...
... Here, Dummett assumes that the minor premiss A is atomic. This assumption is essential, because, according to Dummett’s original definition, a canonical argument must have an atomic conclusion. Prawitz’s counterexample is basically the same (Dummett’s example being an instance thereof) with the dif ...
On the Complexity of Linking Deductive and Abstract Argument
... the two, minimality is generally regarded as an aesthetic criterion, rather than technically essential. Consistency is more important, and of course by relaxing this constraint we admit into our analysis some scenarios that do not seem to have any useful interpretation; but of course this does not i ...
... the two, minimality is generally regarded as an aesthetic criterion, rather than technically essential. Consistency is more important, and of course by relaxing this constraint we admit into our analysis some scenarios that do not seem to have any useful interpretation; but of course this does not i ...
Chapter 2 Propositional Logic
... The terms “sufficient” and “necessary” might sound more or less like having the same meaning, but they have different specific meanings in the world of logic: Definition 15. When p → q, we call p a sufficient condition for q, while q is called a necessary condition for p. Our list of logical operato ...
... The terms “sufficient” and “necessary” might sound more or less like having the same meaning, but they have different specific meanings in the world of logic: Definition 15. When p → q, we call p a sufficient condition for q, while q is called a necessary condition for p. Our list of logical operato ...
AGM Postulates in Arbitrary Logics: Initial Results and - FORTH-ICS
... will be a theory, because under the AGM setting only theories can be KBs. The inclusion postulate guarantees that the operation of contraction will not add any knowledge previously unknown to the KB; this would be irrational, as the contraction operation is used to remove knowledge from a KB. The po ...
... will be a theory, because under the AGM setting only theories can be KBs. The inclusion postulate guarantees that the operation of contraction will not add any knowledge previously unknown to the KB; this would be irrational, as the contraction operation is used to remove knowledge from a KB. The po ...
Revisiting Preferences and Argumentation
... antecedents ϕ1 , . . . , ϕn hold, then without exception, respectively presumably, the consequent ϕ holds’. There are two ways to use these rules: they could encode domain-specific information (as in e.g. default logic) but they could also express general laws of reasoning. For example, the defeasib ...
... antecedents ϕ1 , . . . , ϕn hold, then without exception, respectively presumably, the consequent ϕ holds’. There are two ways to use these rules: they could encode domain-specific information (as in e.g. default logic) but they could also express general laws of reasoning. For example, the defeasib ...
A Taste of Categorical Logic — Tutorial Notes
... is a sequent expressing that the sum of two odd natural numbers is an even natural number. However that is not really the case. The sequent we wrote is just a piece of syntax and the intuitive description we have given is suggested by the suggestive names we have used for predicate symbols (odd, eve ...
... is a sequent expressing that the sum of two odd natural numbers is an even natural number. However that is not really the case. The sequent we wrote is just a piece of syntax and the intuitive description we have given is suggested by the suggestive names we have used for predicate symbols (odd, eve ...
Verification Conditions Are Code - Electronics and Computer Science
... Definition: mges(A, B) gives the most general equalising substitutions to apply to a pair of conditions A, B that result in mgci(A, B) where this exists. For example if mges(A, B) = (α, β) then α(A) = β(B) = mgci(A, B). These definitions are closely related to the notion of unifiers and unification in ...
... Definition: mges(A, B) gives the most general equalising substitutions to apply to a pair of conditions A, B that result in mgci(A, B) where this exists. For example if mges(A, B) = (α, β) then α(A) = β(B) = mgci(A, B). These definitions are closely related to the notion of unifiers and unification in ...
Recursive Predicates And Quantifiers
... of the results stands out more clearly than before. The general theorem asserts that to each of an enumeration of predicate forms, there is a predicate not expressible in that form. The predicates considered belong to elementary number theory. The possibility that this theorem may apply appears when ...
... of the results stands out more clearly than before. The general theorem asserts that to each of an enumeration of predicate forms, there is a predicate not expressible in that form. The predicates considered belong to elementary number theory. The possibility that this theorem may apply appears when ...
A Proof Theory for Generic Judgments
... assumption (that is, on the left of the sequent arrow) is essentially equated to having instead all instances Bt for terms t of type τ . There are cases (one is considered in more detail in Section 6) where we would like to make inferences from an assumption of the form ∀τ x.Bx that holds independen ...
... assumption (that is, on the left of the sequent arrow) is essentially equated to having instead all instances Bt for terms t of type τ . There are cases (one is considered in more detail in Section 6) where we would like to make inferences from an assumption of the form ∀τ x.Bx that holds independen ...
Logic Programming, Functional Programming, and Inductive
... simply specifies the problem — what we want — and the computer works out how to do it. Of course this is an oversimplification. For the declarative languages that exist now, the problem description really is a program: not for any physical machine, but for an abstract machine. A functional program d ...
... simply specifies the problem — what we want — and the computer works out how to do it. Of course this is an oversimplification. For the declarative languages that exist now, the problem description really is a program: not for any physical machine, but for an abstract machine. A functional program d ...
A proof
... first step is the assumption that p is true; subsequent steps are constructed using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we ...
... first step is the assumption that p is true; subsequent steps are constructed using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we ...
Strong Logics of First and Second Order
... To strengthen the logic one narrows the class of test structures hM, Si that are consulted, only now there are two dimensions—one can restrict the firstorder domain M and one can restrict the second-order domain S. The first restriction parallels the first-order case. But even if one allows all poss ...
... To strengthen the logic one narrows the class of test structures hM, Si that are consulted, only now there are two dimensions—one can restrict the firstorder domain M and one can restrict the second-order domain S. The first restriction parallels the first-order case. But even if one allows all poss ...
A Computationally-Discovered Simplification of the Ontological
... us that if there is a unique object in the domain satisfying φ, then the definite description, ıxφ, is well-defined (i.e., has a denotation). A typical instance of Lemma 1 might be y = ıxF x → F y, which asserts that if the object y is identical to the x that is F , then y is F . Lemma 1 can then be ...
... us that if there is a unique object in the domain satisfying φ, then the definite description, ıxφ, is well-defined (i.e., has a denotation). A typical instance of Lemma 1 might be y = ıxF x → F y, which asserts that if the object y is identical to the x that is F , then y is F . Lemma 1 can then be ...
A Computationally-Discovered Simplification of the Ontological
... us that if there is a unique object in the domain satisfying φ, then the definite description, ıxφ, is well-defined (i.e., has a denotation). A typical instance of Lemma 1 might be y = ıxF x → F y, which asserts that if the object y is identical to the x that is F , then y is F . Lemma 1 can then be ...
... us that if there is a unique object in the domain satisfying φ, then the definite description, ıxφ, is well-defined (i.e., has a denotation). A typical instance of Lemma 1 might be y = ıxF x → F y, which asserts that if the object y is identical to the x that is F , then y is F . Lemma 1 can then be ...
Proof Pearl: Defining Functions Over Finite Sets
... The only remaining case is if b 6= c. Here, we define the set D = B − {c}. Trivially B = {c} ∪ D, but we can also show C = {b} ∪ D by subtracting c from both sides of the set equation {b} ∪ B = {c} ∪ C. Because the set D is of smaller cardinality, the induction hypothesis tells us that (D, w ) ∈ fol ...
... The only remaining case is if b 6= c. Here, we define the set D = B − {c}. Trivially B = {c} ∪ D, but we can also show C = {b} ∪ D by subtracting c from both sides of the set equation {b} ∪ B = {c} ∪ C. Because the set D is of smaller cardinality, the induction hypothesis tells us that (D, w ) ∈ fol ...
in every real in a class of reals is - Math Berkeley
... 1 (in N ) is equivalent to its being Proof. Being an N model of T is a 11 in N property and so by our Theorem (relativized to N ) there is even an N -model (N ; M; : : :) of T in which p is not even 11 . (Of course, any type realized in (N ; M; : : :) is recursive in the complete diagram of (N ; M; ...
... 1 (in N ) is equivalent to its being Proof. Being an N model of T is a 11 in N property and so by our Theorem (relativized to N ) there is even an N -model (N ; M; : : :) of T in which p is not even 11 . (Of course, any type realized in (N ; M; : : :) is recursive in the complete diagram of (N ; M; ...
On Countable Chains Having Decidable Monadic Theory.
... satisfy the criterion given in [1]. We proved in [3] that for every chain M = (A, <, P) such that (A, <) contains a sub-interval of type or −, M is not maximal with respect to MSO logic, i.e., there exists an expansion M of M by a predicate which is not MSO definable in M , and such that the MSO ...
... satisfy the criterion given in [1]. We proved in [3] that for every chain M = (A, <, P) such that (A, <) contains a sub-interval of type or −, M is not maximal with respect to MSO logic, i.e., there exists an expansion M of M by a predicate which is not MSO definable in M , and such that the MSO ...
On the specification of sequent systems
... to specify and reason about a variety of proof systems. Since the encodings of such logical systems are natural and direct, the meta-theory of linear logic can be used to draw conclusions about the object-level proof systems. More specifically, in [MP02], the authors present a decision procedure for ...
... to specify and reason about a variety of proof systems. Since the encodings of such logical systems are natural and direct, the meta-theory of linear logic can be used to draw conclusions about the object-level proof systems. More specifically, in [MP02], the authors present a decision procedure for ...
CSE 20 - Lecture 14: Logic and Proof Techniques
... B is 12. How many functions are there from A to B. A B C D E ...
... B is 12. How many functions are there from A to B. A B C D E ...