Inferential Erotetic Logic meets Inquisitive Semantics. Research
... [26] provides a state-of-the-art exposition of IEL. For a concise introduction see [24] or ...
... [26] provides a state-of-the-art exposition of IEL. For a concise introduction see [24] or ...
Back to Basics: Revisiting the Incompleteness
... p.r. axiomatized. This is, in effect, a laborious but routine programming exercise, filling in the details of the procedure we’ve just outlined. Do it for one standard theory, and you’ll be readily convinced that it can be done for any other normally presented axiomatized theory. We’ll say no more a ...
... p.r. axiomatized. This is, in effect, a laborious but routine programming exercise, filling in the details of the procedure we’ve just outlined. Do it for one standard theory, and you’ll be readily convinced that it can be done for any other normally presented axiomatized theory. We’ll say no more a ...
A Logical Foundation for Session
... Over the years, computation systems have evolved from monolithic single-threaded machines to concurrent and distributed environments with multiple communicating threads of execution, for which writing correct programs becomes substantially harder than in the more traditional sequential setting. Thes ...
... Over the years, computation systems have evolved from monolithic single-threaded machines to concurrent and distributed environments with multiple communicating threads of execution, for which writing correct programs becomes substantially harder than in the more traditional sequential setting. Thes ...
Dedukti
... function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicate logic ignores the difference between deduction and computation. For example, when Peano ari ...
... function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicate logic ignores the difference between deduction and computation. For example, when Peano ari ...
Closed Sets of Higher
... When we say that we are taking a less foundational perspective, we mean that we take for granted the existence of sets and functions. In the above example, for instance, we do not concern ourselves with the existence of the operation + (or the existence of R,X, or even function spaces, for that matt ...
... When we say that we are taking a less foundational perspective, we mean that we take for granted the existence of sets and functions. In the above example, for instance, we do not concern ourselves with the existence of the operation + (or the existence of R,X, or even function spaces, for that matt ...
x - Loughborough University Intranet
... A proposition is a linguistic entity that is either true or false. The components of the system are “propositional variables”, that could be interpreted as propositions in some particular piece of discourse. There are two principles - First, the principle of bivalence, proposing that there are exact ...
... A proposition is a linguistic entity that is either true or false. The components of the system are “propositional variables”, that could be interpreted as propositions in some particular piece of discourse. There are two principles - First, the principle of bivalence, proposing that there are exact ...
On perturbations of continuous structures - HAL
... In this paper we define what we call perturbation systems and study their basic properties. These are objects which formalise the intuitive notion of perturbing chosen parts of a continuous logical structure by arbitrarily small amounts. One motivation for this notion is an attempt to generalise an u ...
... In this paper we define what we call perturbation systems and study their basic properties. These are objects which formalise the intuitive notion of perturbing chosen parts of a continuous logical structure by arbitrarily small amounts. One motivation for this notion is an attempt to generalise an u ...
abdullah_thesis_slides.pdf
... Two structures A and B are said to be logically r-equivalent for some r ∈ N, iff they satisfy the same first order formulae of quantifier depth r. Let it be denoted by A ≡r B. We recall that : • If A ≡r B then the Duplicator has a winning strategy for the ...
... Two structures A and B are said to be logically r-equivalent for some r ∈ N, iff they satisfy the same first order formulae of quantifier depth r. Let it be denoted by A ≡r B. We recall that : • If A ≡r B then the Duplicator has a winning strategy for the ...
P,Q
... composite integers for every integer n >0. (I.e. for all n x (x+1,x+2,...x+n) are all composite. Sol: Let x = (n+1)! +1. => x+i = (n+1)! + (i+1) = (i+1)( (n+1)!/(i+1) +1) is composite for i = 1,..,n. QED. Ex 21: [nonconstructive proof] For all n >0 prime number > n. Sol: by contradiction. Assume ...
... composite integers for every integer n >0. (I.e. for all n x (x+1,x+2,...x+n) are all composite. Sol: Let x = (n+1)! +1. => x+i = (n+1)! + (i+1) = (i+1)( (n+1)!/(i+1) +1) is composite for i = 1,..,n. QED. Ex 21: [nonconstructive proof] For all n >0 prime number > n. Sol: by contradiction. Assume ...
ON PERTURBATIONS OF CONTINUOUS STRUCTURES
... In this paper we define what we call perturbation systems and study their basic properties. These are objects which formalise the intuitive notion of perturbing chosen parts of a continuous logical structure by arbitrarily small amounts. One motivation for this notion is an attempt to generalise an u ...
... In this paper we define what we call perturbation systems and study their basic properties. These are objects which formalise the intuitive notion of perturbing chosen parts of a continuous logical structure by arbitrarily small amounts. One motivation for this notion is an attempt to generalise an u ...
On the Complexity of Qualitative Spatial Reasoning: A Maximal
... representation and reasoning where spatial regions are subsets of topological space (Randell et al ., 1992) . Relationships between spatial regions are defined in terms of the relation C(a, b) which is true iff the closure of region a is connected to the closure of region b, i.e . if they share a co ...
... representation and reasoning where spatial regions are subsets of topological space (Randell et al ., 1992) . Relationships between spatial regions are defined in terms of the relation C(a, b) which is true iff the closure of region a is connected to the closure of region b, i.e . if they share a co ...
LTL and CTL - UT Computer Science
... which are true. Formally, a model M, s |= φ is defined inductively as follows: • M, s |= p, if p ∈ AP and p ∈ w(s). • M, s |= ¬φ, if M, s 6|= φ,. • M, s |= ψ ∨ φ, if M, s |= φ or M, s |= ψ. • M, s |= Xφ, if M, s1 |= φ, where s1 is the successor of s. • M, s |= φUψ if there ∃i ≥ 0 such that M, si |= ...
... which are true. Formally, a model M, s |= φ is defined inductively as follows: • M, s |= p, if p ∈ AP and p ∈ w(s). • M, s |= ¬φ, if M, s 6|= φ,. • M, s |= ψ ∨ φ, if M, s |= φ or M, s |= ψ. • M, s |= Xφ, if M, s1 |= φ, where s1 is the successor of s. • M, s |= φUψ if there ∃i ≥ 0 such that M, si |= ...
Predicate logic definitions
... A derivation in PDE is a series of sentences of PLE, each of which is either an assumption or is obtained from previous sentences by one of the rules of PDE. A sentence P of PLE is derivable in PDE from a set Γ of sentences of PLE, written S ` P, iff there exists a derivation in PDE in which all the ...
... A derivation in PDE is a series of sentences of PLE, each of which is either an assumption or is obtained from previous sentences by one of the rules of PDE. A sentence P of PLE is derivable in PDE from a set Γ of sentences of PLE, written S ` P, iff there exists a derivation in PDE in which all the ...
DISCRETE MATHEMATICAL STRUCTURES
... elements is irrelevant, so {a, b} = {b, a}. If the order of the elements is relevant, then we use a different object called ordered pair, represented (a, b). Now (a, b) = (b, a) (unless a = b). In general (a, b) = (a!, b! ) iff a = a! and b = b! . Given two sets A, B, their Cartesian product A × B i ...
... elements is irrelevant, so {a, b} = {b, a}. If the order of the elements is relevant, then we use a different object called ordered pair, represented (a, b). Now (a, b) = (b, a) (unless a = b). In general (a, b) = (a!, b! ) iff a = a! and b = b! . Given two sets A, B, their Cartesian product A × B i ...
The Journal of Functional and Logic Programming The MIT Press
... the same signature. Variables are considered to be in all the signatures; in programming language terminology, they are untyped, at least until the first constraint containing them is processed. From that point on, they can only be bound to terms of a particular domain. Thus, although in one way or ...
... the same signature. Variables are considered to be in all the signatures; in programming language terminology, they are untyped, at least until the first constraint containing them is processed. From that point on, they can only be bound to terms of a particular domain. Thus, although in one way or ...
A BOUND FOR DICKSON`S LEMMA 1. Introduction Consider the
... with and without usage of non-constructive (or “classical”) arguments. The original proof of Dickson [5] and the particularly nice one by Nash-Williams [11] (using minimal bad sequences) are non-constructive, and hence do not immediately provide a bound. But it is well known that by using some logic ...
... with and without usage of non-constructive (or “classical”) arguments. The original proof of Dickson [5] and the particularly nice one by Nash-Williams [11] (using minimal bad sequences) are non-constructive, and hence do not immediately provide a bound. But it is well known that by using some logic ...
Notes on Writing Proofs
... simple as suffice to prove the results we know and love from our calculus days. The reason for choosing few and simple axioms is that there is less chance for a fundamental mistake if we do things this way. Remember, our theorems are only as good as the axioms we base them on. This also makes our re ...
... simple as suffice to prove the results we know and love from our calculus days. The reason for choosing few and simple axioms is that there is less chance for a fundamental mistake if we do things this way. Remember, our theorems are only as good as the axioms we base them on. This also makes our re ...