logic, programming and prolog (2ed)
... starting point is the notion of unification. A unification algorithm is provided and proved correct. Some of its properties are discussed. The unification algorithm is the basis for SLD-resolution which is the only inference rule needed for definite programs. Soundness and completeness of this rule ...
... starting point is the notion of unification. A unification algorithm is provided and proved correct. Some of its properties are discussed. The unification algorithm is the basis for SLD-resolution which is the only inference rule needed for definite programs. Soundness and completeness of this rule ...
Understanding SPKI/SDSI Using First-Order Logic
... An identifier is a word over some given standard alphabet. The set of all identifiers is denoted by A, and an identifier is denoted by A or B (often with subscripts). We assume that both K and A are countable. We do not consider SDSI 1.1 [30] special roots, which are identifiers that are bound to th ...
... An identifier is a word over some given standard alphabet. The set of all identifiers is denoted by A, and an identifier is denoted by A or B (often with subscripts). We assume that both K and A are countable. We do not consider SDSI 1.1 [30] special roots, which are identifiers that are bound to th ...
Labeled Natural Deduction for Temporal Logics
... 1.1 Background and motivation The history of the philosophical and logical reasoning about time goes back at least to ancient Greece, with the works of Aristotle and Diodorus Cronus. However, the birth of modern (symbolic) temporal logic is mainly connected to the name of Prior, who in the late 1950 ...
... 1.1 Background and motivation The history of the philosophical and logical reasoning about time goes back at least to ancient Greece, with the works of Aristotle and Diodorus Cronus. However, the birth of modern (symbolic) temporal logic is mainly connected to the name of Prior, who in the late 1950 ...
THE ULTRAPRODUCT CONSTRUCTION 1. Introduction The
... L which is true for a tuple in A is true for the h-image of the tuple in B. h : A ∼ =B means that h is an isomorphism from A onto B, and A ∼ = B means that A and B are isomorphic. The set of all sentences true in A is called the complete theory of A. A and B are called elementarily equivalent, in sy ...
... L which is true for a tuple in A is true for the h-image of the tuple in B. h : A ∼ =B means that h is an isomorphism from A onto B, and A ∼ = B means that A and B are isomorphic. The set of all sentences true in A is called the complete theory of A. A and B are called elementarily equivalent, in sy ...
Chiron: A Set Theory with Types, Undefinedness, Quotation, and
... also have, but is not required to have, a proof system.) By this definition, a theory in a logic—such as Zermelo-Fraenkel (zf) set theory in first-order order—is itself a logic. But what do we mean by expressivity? There are actually two notions of expressivity. The theoretical expressivity of a logic ...
... also have, but is not required to have, a proof system.) By this definition, a theory in a logic—such as Zermelo-Fraenkel (zf) set theory in first-order order—is itself a logic. But what do we mean by expressivity? There are actually two notions of expressivity. The theoretical expressivity of a logic ...
Notes on Writing Proofs
... composing the first system, we will call points and designate them by the letters A, B, C, . . . ; those of the second, we will call straight lines, and designate them by the letters a, b, c . . . ; and those of the third system, we will call planes and designate them by the Greek letters α, β, γ, . ...
... composing the first system, we will call points and designate them by the letters A, B, C, . . . ; those of the second, we will call straight lines, and designate them by the letters a, b, c . . . ; and those of the third system, we will call planes and designate them by the Greek letters α, β, γ, . ...
1 7.3 calculus with the inverse trigonometric functions
... The three previous sections introduced the ideas of one–to–one functions and inverse functions and used those ideas to define arcsine, arctangent, and the other inverse trigonometric functions. Section 7.3 presents the calculus of inverse trigonometric functions. In this section we obtain d ...
... The three previous sections introduced the ideas of one–to–one functions and inverse functions and used those ideas to define arcsine, arctangent, and the other inverse trigonometric functions. Section 7.3 presents the calculus of inverse trigonometric functions. In this section we obtain d ...
Teach Yourself Logic 2017: A Study Guide
... for further work – the core chapters of these cover the so-called ‘baby logic’ that it would be ideal for a non-mathematician to have under his or her belt: 1. My Introduction to Formal Logic* (CUP 2003: a second edition is in preparation): for more details see the IFL pages, where there are also an ...
... for further work – the core chapters of these cover the so-called ‘baby logic’ that it would be ideal for a non-mathematician to have under his or her belt: 1. My Introduction to Formal Logic* (CUP 2003: a second edition is in preparation): for more details see the IFL pages, where there are also an ...
The Development of Categorical Logic
... (1995) such structures are termed Zermelo-Fraenkel algebras. They show how to define V(A) when A is an object in a topos E. For this, it was necessary to specify what the term “set-indexed” should be taken to mean in the definition of completeness, for if all the objects of E were to be regarded as ...
... (1995) such structures are termed Zermelo-Fraenkel algebras. They show how to define V(A) when A is an object in a topos E. For this, it was necessary to specify what the term “set-indexed” should be taken to mean in the definition of completeness, for if all the objects of E were to be regarded as ...
![arXiv:1512.05177v1 [cs.LO] 16 Dec 2015](http://s1.studyres.com/store/data/012886476_1-5eedb3c008e9a2ffa0e571a06be0b669-300x300.png)
arXiv:1512.05177v1 [cs.LO] 16 Dec 2015
... Our contributions Firstly, we describe translations from VPAs to VLDL and vice versa. For the direction from automata to logic we use a translation of VPAs into deterministic parity stair automata (PSA) by Löding et al. [12], which we then translate into VLDL formulas. For the direction from logic ...
... Our contributions Firstly, we describe translations from VPAs to VLDL and vice versa. For the direction from automata to logic we use a translation of VPAs into deterministic parity stair automata (PSA) by Löding et al. [12], which we then translate into VLDL formulas. For the direction from logic ...
Hybrid, Classical, and Presuppositional Inquisitive Semantics
... logical language and specific sentences of a specific natural language. • The inherent claim is that there is a fundamental correspondence between the interpretation of the semantic operations in the logical language and constructions in natural language that involve informative and inquisitive cont ...
... logical language and specific sentences of a specific natural language. • The inherent claim is that there is a fundamental correspondence between the interpretation of the semantic operations in the logical language and constructions in natural language that involve informative and inquisitive cont ...
Notes on the Science of Logic
... then reliance on arithmetic or geometrical intuitions would be reasonable; but instead our principal aim is the logical one of seeing how, using only quantifier and truth-functional principles, our conclusions follow from the fundamental axioms and definitions that characterize our subject matter. F ...
... then reliance on arithmetic or geometrical intuitions would be reasonable; but instead our principal aim is the logical one of seeing how, using only quantifier and truth-functional principles, our conclusions follow from the fundamental axioms and definitions that characterize our subject matter. F ...
LOGIC I 1. The Completeness Theorem 1.1. On consequences and
... of terms t, that we have M |= t = c if and only if t = c is in S. So consider a term t = f (t1 , . . . , tn ). By the same argument as above, there is a constant c and constants c1 , . . . , cn such that f (t1 , . . . , tn ) = c and ti = ci are all in S. By the inductive assumption, we have that M | ...
... of terms t, that we have M |= t = c if and only if t = c is in S. So consider a term t = f (t1 , . . . , tn ). By the same argument as above, there is a constant c and constants c1 , . . . , cn such that f (t1 , . . . , tn ) = c and ti = ci are all in S. By the inductive assumption, we have that M | ...
a PDF file of the textbook - U of L Class Index
... The first of these deductions is very famous, but the second one is lame. It may seem odd to even call it a deduction, because the two hypotheses have nothing at all to do with the conclusion, but, given our definition, it does count as a deduction. However, it is is a very poor one, so it cannot be ...
... The first of these deductions is very famous, but the second one is lame. It may seem odd to even call it a deduction, because the two hypotheses have nothing at all to do with the conclusion, but, given our definition, it does count as a deduction. However, it is is a very poor one, so it cannot be ...
