PROBLEM SOLVING THROUGH FIRST-ORDER LOGIC
... logical connectives and incorporating quantifiers. Atoms are predicates (standard or infix) and they are represented by id terms e.g. child(mary, john), where child is a predicate name and mary and john are terms or X < 3. It is important to mention, that the difference between id term and term (in ...
... logical connectives and incorporating quantifiers. Atoms are predicates (standard or infix) and they are represented by id terms e.g. child(mary, john), where child is a predicate name and mary and john are terms or X < 3. It is important to mention, that the difference between id term and term (in ...
An admissible second order frame rule in region logic
... occur in various important design patterns [10]. The mismatch enabled by a discipline is made explicit in a second order frame rule adapted from that of separation logic [17]. The ordinary frame rule of separation logic resembles the Invariance rule, but without using a side condition for absence of ...
... occur in various important design patterns [10]. The mismatch enabled by a discipline is made explicit in a second order frame rule adapted from that of separation logic [17]. The ordinary frame rule of separation logic resembles the Invariance rule, but without using a side condition for absence of ...
Nelson`s Strong Negation, Safe Beliefs and the - CEUR
... While the answer set semantics has been extended to always more flexible classes of logic programs where conjunctions, disjunctions and default negations are allowed to occur unrestrictedly in any part of the formulas, strong negation has remained tied to the atomic level. In some cases, to compute ...
... While the answer set semantics has been extended to always more flexible classes of logic programs where conjunctions, disjunctions and default negations are allowed to occur unrestrictedly in any part of the formulas, strong negation has remained tied to the atomic level. In some cases, to compute ...
A Contraction-free and Cut-free Sequent Calculus for
... From the point of view of Hilbert systems, propositional dynamic logic is well-defined. Indeed, there are several equivalent axiomatisations of P DL (see for example [4, 7]), each of which is obtained by adding to classical propositional logic: (i) the distribution axiom schema, that now has the form ...
... From the point of view of Hilbert systems, propositional dynamic logic is well-defined. Indeed, there are several equivalent axiomatisations of P DL (see for example [4, 7]), each of which is obtained by adding to classical propositional logic: (i) the distribution axiom schema, that now has the form ...
THE ABUNDANCE OF THE FUTURE A Paraconsistent Approach to
... a proposition is true if the event corresponding to it has at least some degree of probability, i.e. if we can rationally bet on it. Notwithstanding the fact that the semantics we present here is purely qualitative, a probabilistic interpretation of it will shed light on its paraconsistent features, ...
... a proposition is true if the event corresponding to it has at least some degree of probability, i.e. if we can rationally bet on it. Notwithstanding the fact that the semantics we present here is purely qualitative, a probabilistic interpretation of it will shed light on its paraconsistent features, ...
Logic for Computer Science. Lecture Notes
... reasoning or, in other words, what are we going to talk about and what language are we going to use. The next step is to associate a precise meaning to basic notions of the language, in order to avoid ambiguities and misunderstandings. Finally we have to state clearly what kind of opinions (sentence ...
... reasoning or, in other words, what are we going to talk about and what language are we going to use. The next step is to associate a precise meaning to basic notions of the language, in order to avoid ambiguities and misunderstandings. Finally we have to state clearly what kind of opinions (sentence ...
Automated Deduction
... It is worthwhile to start these course notes by giving a brief outline of the history of concepts which are fundamental to the area of automated deduction. Even though this outline is quite superficial it nevertheless serves to illustrate how old many of the ideas and concepts at the base of automat ...
... It is worthwhile to start these course notes by giving a brief outline of the history of concepts which are fundamental to the area of automated deduction. Even though this outline is quite superficial it nevertheless serves to illustrate how old many of the ideas and concepts at the base of automat ...
Version 1.5 - Trent University
... and determine their truth. The real fun lies in the relationship between interpretation of statements, truth, and reasoning. This volume develops the basics of two kinds of formal logical systems, propositional logic and first-order logic. Propositional logic attempts to make precise the relationshi ...
... and determine their truth. The real fun lies in the relationship between interpretation of statements, truth, and reasoning. This volume develops the basics of two kinds of formal logical systems, propositional logic and first-order logic. Propositional logic attempts to make precise the relationshi ...
Classical Logic and the Curry–Howard Correspondence
... due (or attributed) to Euclid, where a derivation would begin with axioms and proceed line by line, with each line derived from those preceding it by means of some inference rule. Nowadays such logics are known as ‘Hilbert systems’. This format can be somewhat cumbersome and inelegant, both because ...
... due (or attributed) to Euclid, where a derivation would begin with axioms and proceed line by line, with each line derived from those preceding it by means of some inference rule. Nowadays such logics are known as ‘Hilbert systems’. This format can be somewhat cumbersome and inelegant, both because ...
How Does Resolution Works in Propositional Calculus and
... express it. The propositional logic is not powerful enough to represent all types of assertions that are used in computer science and mathematics, or to express certain types of relationship between propositions such as equivalence. For example, the assertion "x is greater than 1", where x is a vari ...
... express it. The propositional logic is not powerful enough to represent all types of assertions that are used in computer science and mathematics, or to express certain types of relationship between propositions such as equivalence. For example, the assertion "x is greater than 1", where x is a vari ...
A Crevice on the Crane Beach: Finite-Degree
... Are all neutral letter languages of FO[ARB] in FO[≤]? Note that this echoes the above intuition on uniformity, since the numerical predicates correspond precisely to the allowed power to compute the circuit for a given input length [11]. The intuition on the logic side is even more compelling: if a ...
... Are all neutral letter languages of FO[ARB] in FO[≤]? Note that this echoes the above intuition on uniformity, since the numerical predicates correspond precisely to the allowed power to compute the circuit for a given input length [11]. The intuition on the logic side is even more compelling: if a ...
Restricted notions of provability by induction
... This assumption, as stated, is rather imprecise and needs some elaboration. What we mean by “feasibility” is the possibility of an implementation which solves the task successfully on contemporary hardware in a reasonable amount of time. This notion is quite standard in computer science and we beli ...
... This assumption, as stated, is rather imprecise and needs some elaboration. What we mean by “feasibility” is the possibility of an implementation which solves the task successfully on contemporary hardware in a reasonable amount of time. This notion is quite standard in computer science and we beli ...
page 3 A CONVERSE BARCAN FORMULA IN ARISTOTLE`S
... To avoid clutter parentheses and brackets will often not be used in the presentation of the simple assertoric forms. ...
... To avoid clutter parentheses and brackets will often not be used in the presentation of the simple assertoric forms. ...
Glivenko sequent classes in the light of structural proof theory
... transfers from classical to intuitionistic provability therefore fall under the nomenclature of Glivenko-style results: these are results about classes of formulas for which classical provability gives intuitionistic provability. The interest in isolating such classes lies in the fact that it may be ...
... transfers from classical to intuitionistic provability therefore fall under the nomenclature of Glivenko-style results: these are results about classes of formulas for which classical provability gives intuitionistic provability. The interest in isolating such classes lies in the fact that it may be ...
Implicit Hitting Set Algorithms for Reasoning Beyond NP
... In this section we generalize the MaxHS algorithm and its components into a general framework for developing implicit hitting set algorithms. As a core ingredient we need a general problem setting suitable for many contexts, which we introduce next. We assume a set of (domain) elements L and a predi ...
... In this section we generalize the MaxHS algorithm and its components into a general framework for developing implicit hitting set algorithms. As a core ingredient we need a general problem setting suitable for many contexts, which we introduce next. We assume a set of (domain) elements L and a predi ...
Problems in Applying Peirce to Social Sciences
... sciences. In particular, I wish to show that Peirce’s philosophy has some new things to say in regard to the hoary question of what human rationality is all about. I take the same course that the history of sociology has originally taken, by first taking critical issue, with the help of Peirce, with ...
... sciences. In particular, I wish to show that Peirce’s philosophy has some new things to say in regard to the hoary question of what human rationality is all about. I take the same course that the history of sociology has originally taken, by first taking critical issue, with the help of Peirce, with ...
PDF
... Immerman suggested a new logic FO + IFP + C extending FO + IFP with a counting construct (Immerman (1986)). But even this logic fails to capture PTIME, as has been proved by Cai et al. (1992). Abiteboul and Vianu de ned another extension of FO + IFP, called FO + IFP + W, which has a nondeterministic ...
... Immerman suggested a new logic FO + IFP + C extending FO + IFP with a counting construct (Immerman (1986)). But even this logic fails to capture PTIME, as has been proved by Cai et al. (1992). Abiteboul and Vianu de ned another extension of FO + IFP, called FO + IFP + W, which has a nondeterministic ...
Applying Peirce to Social Studies – Some Do`s and Don`ts
... sciences. In particular, I wish to show that Peirce’s philosophy has some new things to say in regard to the hoary question of what human rationality is all about. I take the same course that the history of sociology has originally taken, by first taking critical issue, with the help of Peirce, with ...
... sciences. In particular, I wish to show that Peirce’s philosophy has some new things to say in regard to the hoary question of what human rationality is all about. I take the same course that the history of sociology has originally taken, by first taking critical issue, with the help of Peirce, with ...
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 ...
Identity in modal logic theorem proving
... In the realm of modal logics, almost all presentations of the logic of these systems are given in terms of axioms. But no one who is interested in providing automated proofs within modal logic uses an axiomatic system, and so it would therefore seem that all these methods of implementing t h e m mus ...
... In the realm of modal logics, almost all presentations of the logic of these systems are given in terms of axioms. But no one who is interested in providing automated proofs within modal logic uses an axiomatic system, and so it would therefore seem that all these methods of implementing t h e m mus ...
The Diagonal Lemma Fails in Aristotelian Logic
... all the laws of the traditional syllogism will hold. (Strawson, 1952, p. 173) Traditional logic assumes that the subject term refers to something that does exist. However, the formulae in Table 2 are implausible translations of the natural language sentences. (Strawson, 1952, p. 173) So he proposed ...
... all the laws of the traditional syllogism will hold. (Strawson, 1952, p. 173) Traditional logic assumes that the subject term refers to something that does exist. However, the formulae in Table 2 are implausible translations of the natural language sentences. (Strawson, 1952, p. 173) So he proposed ...
Formal logic
... Logic studies the validity of arguments. A typical case in point is that of syllogisms: logical arguments in which, starting from two premises, a conclusion is reached. For example, given that There are horses in Spain. All horses are mammals. it can be inferred that There are mammals in Spain. Of c ...
... Logic studies the validity of arguments. A typical case in point is that of syllogisms: logical arguments in which, starting from two premises, a conclusion is reached. For example, given that There are horses in Spain. All horses are mammals. it can be inferred that There are mammals in Spain. Of c ...
Predicate logic. Formal and informal proofs
... and easy to assign • The truth of other statements may not be obvious, … …. But it may still follow (be derived) from known facts about the world To show the truth value of such a statement following from other statements we need to provide a correct supporting argument - a proof Important questions ...
... and easy to assign • The truth of other statements may not be obvious, … …. But it may still follow (be derived) from known facts about the world To show the truth value of such a statement following from other statements we need to provide a correct supporting argument - a proof Important questions ...
Sequent-Systems for Modal Logic
... A rule, axiom or axiom-schema is eliminablefrom a system S if the subsystem of S without this rule, axiom or axiom-schema has the same theorems as S. It can easily be shown that a rule R is admissible in a system S iff it is eliminable from the extension of S with R. Our aim now is to show that D is ...
... A rule, axiom or axiom-schema is eliminablefrom a system S if the subsystem of S without this rule, axiom or axiom-schema has the same theorems as S. It can easily be shown that a rule R is admissible in a system S iff it is eliminable from the extension of S with R. Our aim now is to show that D is ...
Subset Types and Partial Functions
... This paper develops a unified approach to partial functions and subset types, which does not suffer from this anomalous behavior. We begin with a higherorder logic that allows functions to be undefined on some arguments. We extend this logic’s type system to include subset types, but we retain deci ...
... This paper develops a unified approach to partial functions and subset types, which does not suffer from this anomalous behavior. We begin with a higherorder logic that allows functions to be undefined on some arguments. We extend this logic’s type system to include subset types, but we retain deci ...