higher-order logic - University of Amsterdam
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
PDF
... of the statements that can be derived by means of the formal rules (or, what amounts to the same, how they are understood) because understanding a language, even a formal one, is not merely to understand its rules as rules of symbol manipulation. Believing that is the mistake of formalism.” The firs ...
... of the statements that can be derived by means of the formal rules (or, what amounts to the same, how they are understood) because understanding a language, even a formal one, is not merely to understand its rules as rules of symbol manipulation. Believing that is the mistake of formalism.” The firs ...
A Survey on Small Fragments of First-Order Logic over Finite
... class, there seems to be little knowledge in a broad community. A reason for this is that the proofs are spread over the literature and even in the survey [76] many proofs are referred to the original literature which in turn is sometimes quite difficult to read. ...
... class, there seems to be little knowledge in a broad community. A reason for this is that the proofs are spread over the literature and even in the survey [76] many proofs are referred to the original literature which in turn is sometimes quite difficult to read. ...
The Expressive Power of Modal Dependence Logic
... Dependence is a central notion in many scientific disciplines. For example in physics there are dependences in experimental data. Decision theory is concerned with identifying the variables on which the result depends. Furthermore, dependences between attributes is a key notion in database theory. I ...
... Dependence is a central notion in many scientific disciplines. For example in physics there are dependences in experimental data. Decision theory is concerned with identifying the variables on which the result depends. Furthermore, dependences between attributes is a key notion in database theory. I ...
Gödel`s Incompleteness Theorems
... This theorem is quite remarkable in its own right because it shows that Peano’s well-known postulates, which by and large are considered as an axiomatic basis for elementary arithmetic, cannot prove all true statements about natural numbers. But Gödel went even further. He showed that his first inc ...
... This theorem is quite remarkable in its own right because it shows that Peano’s well-known postulates, which by and large are considered as an axiomatic basis for elementary arithmetic, cannot prove all true statements about natural numbers. But Gödel went even further. He showed that his first inc ...
Outlier Detection Using Default Logic
... 1 Introduction Default logics were developed as a tool for reasoning with incomplete knowledge. By using default rules, we can describe how things work in general and then make some assumptions about individuals and draw conclusions about their properties and behavior. In this paper, we suggest a so ...
... 1 Introduction Default logics were developed as a tool for reasoning with incomplete knowledge. By using default rules, we can describe how things work in general and then make some assumptions about individuals and draw conclusions about their properties and behavior. In this paper, we suggest a so ...
1992-Ideal Introspective Belief
... Here, rather than defining restrictions on extensions, we have taken the approach of trying to find the minimal reflective principles that will allow an agent full knowledge of his beliefs, at the same time trying to make them as grounded as possible. The result is a logic that is somewhere between ...
... Here, rather than defining restrictions on extensions, we have taken the approach of trying to find the minimal reflective principles that will allow an agent full knowledge of his beliefs, at the same time trying to make them as grounded as possible. The result is a logic that is somewhere between ...
Intuitionistic modal logic made explicit
... Justification logics are explicit modal logics in the sense that they unfold the -modality in families of so-called justification terms. Instead of formulas A, meaning that A is known, justification logics include formulas t : A, meaning that A is known for reason t. Artemov’s original semantics f ...
... Justification logics are explicit modal logics in the sense that they unfold the -modality in families of so-called justification terms. Instead of formulas A, meaning that A is known, justification logics include formulas t : A, meaning that A is known for reason t. Artemov’s original semantics f ...
On Provability Logic
... on the (from our point of view) most interesting facts and ideas about provability logic and mention their applications in metamathematics. We put stress on the use of Gentzen calculus for provability logic invented in Sambin and Valentini 1982. We present no new results and we omit all difficult pr ...
... on the (from our point of view) most interesting facts and ideas about provability logic and mention their applications in metamathematics. We put stress on the use of Gentzen calculus for provability logic invented in Sambin and Valentini 1982. We present no new results and we omit all difficult pr ...
Verification Conditions Are Code - Electronics and Computer Science
... Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from the associativity of function composition. Working directly with program semantics is a model-theoretic approach, howev ...
... Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from the associativity of function composition. Working directly with program semantics is a model-theoretic approach, howev ...
Interpreting and Applying Proof Theories for Modal Logic
... The identity axioms, the basic structural rules, the logical rules ¬L, ¬R, ∧L and ∧R, the modal rules L and R, plus the classical structural rules of weakening, contraction and cut, form the Display proof system for the basic normal modal logic K. In order to obtain display calculi for other modal ...
... The identity axioms, the basic structural rules, the logical rules ¬L, ¬R, ∧L and ∧R, the modal rules L and R, plus the classical structural rules of weakening, contraction and cut, form the Display proof system for the basic normal modal logic K. In order to obtain display calculi for other modal ...
Let me begin by reminding you of a number of passages ranging
... “My Basic Logical Insights” very seriously. Indeed, I am inclined to give them a certain pride of place when it comes to understanding Frege’s distinctive understanding of the nature and status of logic. What remains to be seen is whether, or to what extent, we can reconcile these remarks with his o ...
... “My Basic Logical Insights” very seriously. Indeed, I am inclined to give them a certain pride of place when it comes to understanding Frege’s distinctive understanding of the nature and status of logic. What remains to be seen is whether, or to what extent, we can reconcile these remarks with his o ...
this PDF file
... the logic in question) and lacking a given formula has a negation-consistent, complete subtheory with all theorems (of the logic in question) lacking the same formula (cf., e.g., [3]). Proof of this fact (Lemma 4) for relevant logics including TWcrγ is provided in Section 3 of the paper, its main se ...
... the logic in question) and lacking a given formula has a negation-consistent, complete subtheory with all theorems (of the logic in question) lacking the same formula (cf., e.g., [3]). Proof of this fact (Lemma 4) for relevant logics including TWcrγ is provided in Section 3 of the paper, its main se ...
Lecture notes from 5860
... of the statements that can be derived by means of the formal rules (or, what amounts to the same, how they are understood) because understanding a language, even a formal one, is not merely to understand its rules as rules of symbol manipulation. Believing that is the mistake of formalism.” The firs ...
... of the statements that can be derived by means of the formal rules (or, what amounts to the same, how they are understood) because understanding a language, even a formal one, is not merely to understand its rules as rules of symbol manipulation. Believing that is the mistake of formalism.” The firs ...
MoggiMonads.pdf
... [Sco69, GMW79]), that can be found only after developing a semantics based on mathematical structures rather than term models, but it does not give clear criteria to single out the general principles among the properties satisfied by the model. Moreover, the theory at the heart of Denotational Seman ...
... [Sco69, GMW79]), that can be found only after developing a semantics based on mathematical structures rather than term models, but it does not give clear criteria to single out the general principles among the properties satisfied by the model. Moreover, the theory at the heart of Denotational Seman ...
Redundancies in the Hilbert-Bernays derivability conditions for
... The elimination of the first derivability condition allows the application of the Consistency Theorem to cut-free logics which cannot prove that they are closed under cut. It is Theorem 1 which will probably have primary interest for readers who are not concerned with technical proof theory or with ...
... The elimination of the first derivability condition allows the application of the Consistency Theorem to cut-free logics which cannot prove that they are closed under cut. It is Theorem 1 which will probably have primary interest for readers who are not concerned with technical proof theory or with ...
full text (.pdf)
... We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models. As a corollary we obtain a comple ...
... We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models. As a corollary we obtain a comple ...
How Does Resolution Works in Propositional Calculus and
... calculus. Some statements are there in real life situation which are correct but proposition logic fail to express them. To overcome this deficiency predicate logic has been introduced. For example: in real life statement- “All mammals suckle their young ones. Since elephant is a mammal, it suckles ...
... calculus. Some statements are there in real life situation which are correct but proposition logic fail to express them. To overcome this deficiency predicate logic has been introduced. For example: in real life statement- “All mammals suckle their young ones. Since elephant is a mammal, it suckles ...
Modular Sequent Systems for Modal Logic
... k-rule is not invertible. It is of course easy to drop contraction and build it into the k-rule and into the rules in Ẋ, which makes all rules invertible. The reason we choose not to do this is because our cut-elimination procedure works better with explicit contraction. There are also some rules t ...
... k-rule is not invertible. It is of course easy to drop contraction and build it into the k-rule and into the rules in Ẋ, which makes all rules invertible. The reason we choose not to do this is because our cut-elimination procedure works better with explicit contraction. There are also some rules t ...
Definability properties and the congruence closure
... Sxyq~(x, y)<,~o(x, y) defines a Souslin tree, Gxyzq)(x, y, z)<:~o(x, y, z) defines the operation of a finitely generated group, R~,Xl,..., x,q)(xl,..., x,)<*there is a set of x indiscernibles for ~0 in the field of ~o, and we show, via a uniform counterexample, that both properties fail for any regu ...
... Sxyq~(x, y)<,~o(x, y) defines a Souslin tree, Gxyzq)(x, y, z)<:~o(x, y, z) defines the operation of a finitely generated group, R~,Xl,..., x,q)(xl,..., x,)<*there is a set of x indiscernibles for ~0 in the field of ~o, and we show, via a uniform counterexample, that both properties fail for any regu ...
A Nonstandard Approach to the. Logical Omniscience Problem
... approach, validity and logical consequence are taken with respect to only the standard worlds, where all the rules of standard logic hold. For example, a formula is valid exactly if it is true in all the standard worlds in every structure. The intuition here is that the nonstandard worlds serve only ...
... approach, validity and logical consequence are taken with respect to only the standard worlds, where all the rules of standard logic hold. For example, a formula is valid exactly if it is true in all the standard worlds in every structure. The intuition here is that the nonstandard worlds serve only ...
Proof theory for modal logic
... literature. In addition to these difficulties, modal logic has a context-dependent rule (the rule of necessitation) that cannot be applied to arbitrary derivations. It is therefore not surprising that the search for a normalizing system for the full language of modal logic, with a subformula propert ...
... literature. In addition to these difficulties, modal logic has a context-dependent rule (the rule of necessitation) that cannot be applied to arbitrary derivations. It is therefore not surprising that the search for a normalizing system for the full language of modal logic, with a subformula propert ...
Strong Completeness for Iteration
... T X. We formalise such constructs using natural operations on functors. We also note that PDL and GL are usually interpreted over so-called standard models, in which the program/game constructs have a certain intended meaning. In our general framework this leads to the notion of a standard model rel ...
... T X. We formalise such constructs using natural operations on functors. We also note that PDL and GL are usually interpreted over so-called standard models, in which the program/game constructs have a certain intended meaning. In our general framework this leads to the notion of a standard model rel ...
Propositions as Types - Informatics Homepages Server
... cursive function is λ-definable, and vice-versa. The proof was outlined by Church [8] and published in detail by Kleene [36]. Rather than mollifying Gödel, this result caused him to doubt that his own definition was correct! Things stood at an impasse. Meanwhile, at Cambridge, Alan Turing, a studen ...
... cursive function is λ-definable, and vice-versa. The proof was outlined by Church [8] and published in detail by Kleene [36]. Rather than mollifying Gödel, this result caused him to doubt that his own definition was correct! Things stood at an impasse. Meanwhile, at Cambridge, Alan Turing, a studen ...
Jesús Mosterín
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Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.